UC-NRLF 


SB    Et    Ebl 


LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 

Deceived         JAN     11  1893 ....  189 
^Accessions  No.  IfQOif  \T~.  Class  No. 


JIITI-ESIT 


PRACTICAL  TREATISE 


CONSTRUCTION 


IRON  HIGHWAY  BRIDGES 


USE   OF   TOWN   COMMITTEES. 


TOGETHER  WITH  A 


SHORT  ESSAY  UPON  THE  APPLICATION  OF  THE  PRINCIPLES  OF  THE 

LEVER  TO  A  READY  ANALYSIS  OF  THE   STRAINS  UPON  THE 

MORE   CUSTOMARY  FORMS   OF  BEAMS  AND  TRUSSES. 


BY 

ALFRED    P.    ROLLER,    A.M., 

1 1 

CIVIL    ENGINEER, 

MEMBER    OF    THE    AM.     SOC.     CIV.     ENGINEERS. 


FOURTH  EDITION. 


NEW   YORK: 
JOHN   WILEY   AND   SONS, 

53  EAST  TENTH  STREET, 

Second  door  west  of  Broadway. 

i8c 


Entered,  according  to  Act  of  Congress,  in  the  year  1876,  by 

ALFRED   P.  BOLLER, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


DEDICATION. 


TO 
TOWN    COMMITTEES,  SELECTMEN,  COUNTY    FREEHOLDERS, 

AND 

OTHER    PUBLIC    OFFICERS, 

TO  WHOM    IS    INTRUSTED  THE    RESPONSIBILITY  OF 

ERECTING  "IRON  BRIDGES,"   THIS    BOOK    IS 

RESPECTFULLY    DEDICATED 

BY 

THE   AUTHOR. 


INDEX. 

PART    I. 

GENERAL  AND  DESCRIPTIVE. 

SkOX 

2Ebthetical  Effect  w.  Plain  Utility 87 

American  and  Riveted  Systems  Compared ,  61 

Angle  Iron 26 

Angle  Irons,  Section  of,  how  Determined 64 

Architecture  of  Bridge  Building 82 

Asphalt,  Weight  of    79 

Author's  Bridge Frontispiece. 

Beam  Bridges 74 

•'          "      PlankFloor 75 

"          "      Wood  Pavement  on  Buckle  Plates 75 

*'          "      Telford  Pavement  on  Brick  Arches 76 

Bearings  and  Connections,  Machine  Made 47 

Bolster  Pieces 71 

Braces,  Main  and  Counter  ....    33 

"        Proportions  of 33 

Bracing,  Horizontal 67 

"        Sway 67 

Brick  Work,  Weight  of 79 

Bridge  Settings 90-96 

« '        Platforms '. 74 

Bridges,  General  Rules  for  Selection  of 43 

"        How  Classified 32 

"        Kinds  of 32 

«'        Selectionof 43 

Buckle  Plate  for  Floor 73 

Cast  Iron 28 

Chords,  Strains  in 32 

'«        TheirOffice         32 

Cincinnati  Bridge  Co.'s  Bridge 90 

Columns,  Cast  Iron,  Formula  for  their  Strength 57 

44         Table  of  Breaking  Strer  gth  for  Cast  and  Wrought  Iron 58 

With  Square  Ends  and  with  Round  Ends 66 

"         Wrought  Iron  Formula  for  Strength 57 


Tl  INDEX. 

PAGE 

Compound  Riveted  Girder 64 

Concrete,  Weight  of , . , . .  79 

Construction,  Methods  of 44 

Counter  Braces,  their  Action 33 

Corrugated  Plate  for  Floor 73 

Cross  Beams 63 

Decoration,  Constructed 83-84 

Detroit  Bridge  Co.'s  Bridge 96 

Elasticity,  Limit  of 12 

End  Struts,  Method  of  Adding  to  Architectural  Effect 85 

Eye-Bars 51 

«*         Their  Manufacture 53 

Factor  of  Safety. 11 

Fairmount  Bridge 83 

Fastening  Iron  Stringers  to  Floor  Beams 69 

Fink  Suspension  Truss 41 

Floor-Beams 63 

"             Factor  of  Safety  for 16 

"             Rivetingof 65 

•'             Their  Connection 66 

Floor,  General  Type  of,  for  Road  Bridges 71-72 

Flooring 69 

"        Examples  of  Permanent 73-74 

"        System 62 

Floor  Planks,  Method  of  Laying 70 

Floor  Plates,  Forms  of  Wrought  Iron,  Illustrated . . . . . 73 

"             Wrought  Iron 73 

Form  of  Specifications  in  Bridge  Letting 93 

Framing,  American  System 47 

Girard  Avenue  Bridge 84 

Girders,  Apparent  Stiffness  of 62 

"        Compound  Riveted 34 

"       Depthof .... 64 

"       Solid  Rolled 34 

Good  Bridge,  Elements  of 11 

Gordon's  Formula,  Modification  of , 57 

Gravel,  Weight  of 79 

Guard  Timbers 71 

Hangers,  Best  Form  of 65 

"        Factor  of  Safety  to  be  Used 67 

Height  of  Truss  when  Sway  Bracing  is  Used 78 

Inclined  Struts,  Architectural  Effect 86 

Invitation  to  Bridge  Builders,  Form  of 93 

Iron,  Cast 27 

"        "  Cold-Short 27 


INDEX.  vii 

fl 

PAQB 

Iron,  Cast,  Cold-Short,  Distinctive  Features  of 27 

"        "  Danger  from  Cross  Strains 28 

"        ««   Red-Short 27 

"        *•         "          Distinctive  Features  of 27 

"        "  Test  by  Short  and  Long  Grooves 27 

"        "  WhentobeUsed 28 

44    Decarburizing  of 19 

44    Grey 18 

44    Large  and  Small  Specimens,  Testing  of 26 

4  4    Manufacture 17 

"    Ordnance 29 

44    Pig,  Grades  of 18 

4'    White 18 

44    Work,  Examination  of 80 

41        44     'Maintenance 79 

«4        44      Method  of  Avoiding  Rust 76 

*4        "      Painting  of 80 

44        44      Removal  of  Scale 80 

44    Wrought ' 21 

"          "        Elastic  Limit  of 25 

4'          "        Grades  of 26 

Joint  Box,  Cast  Iron,  Advantages  of 60 

King  Post  Truss 85 

Lattice-Truss  or  Double  Triangular 40 

Loads  on  Bridges. ...  * ....  14 

Loading,  Table  of,  Proportioned  to  Span 15 

Material,  True  Value  of 12 

Materials  of  Construction 17 

Needle  Beams 63 

Panel,  Length  of 33 

"    Point 33 

Pavement  Blocks 74 

Pig-Iron,  Grades  of 18 

44         Manufacture  of 19 

Pins  and  Eyes 49 

Pins,  Benders'  Theory 49-50 

Pin  Holes,  Boring  of 61 

Plainfield  Bridge,  Section  of 63 

44            "          SideViewof 63 

Plank  for  Flooring,  Method  of  Laying 31 

"     Layingof , 30 

Planks  protected  against  Sun-Cracking 72 

Plate,  Bar  and  Angle  Iron 26 

Plate  Iron , 26 

Posts,  Connection.... K 


viii  INDEX. 

PAGE 

Posts,  Sections  of,  Illustrated 65 

"    Strength  of ? 56 

"    Their  Resisting  Power. 55 

Queen  Post  Truss 36 

Rail  Base,  when  to  be  Used 71 

Riveted  Work 45 

"        System,  how  to  Use  it *. 61 

Rivets,  their  Pitch 65 

Riveting,  Hand  and  Power 46-47 

Sap  Wood 30 

Screw  Ends. 54 

Shoes  or  Bases 55 

Sidewalks,  Drainage  of 71 

"         Method  of  Laying 71 

Specifications  for  Bridges 93 

Strains,  Kinds  of 82 

Strength  of  Cast  and  Wrought  Iron  Columns,  Table  of 58 

Stringer  Beams 67 

Stringers,  Factor  of  Safety  for 16 

u         Iron 68 

"         Tables  of,  Proportioned  to  Wheel-Loads 69 

"         Timber  to  be  Used 68 

"        Wooden 68 

Struts 33 

"     andTies 33 

Strut  Tie 33 

Testing  of  Bridges 88-90 

Thin  Webs,  Precautions  if  Used 65 

Ties 33 

Timber  for  Stringers,  Inspection  of 31 

"       Kindsof 31 

"       Merchantable 29 

"       Preservation  of 31 

"       Quality  of 29 

Timber,  Season  Cracks,  Heart  Cracks 30 

Top  Chord  Section,  Kinds  of  Joints 59 

Top  Chord  Sections,  \  Riveted   S^stem  nitrated,  ,  ^ 
(  For  Pin  Connections                  ) 

Truss  Bridge,  its  Architectural  Effect 84-85 

Truss  Bridges 34 

Trusses  in  Tension  and  Compression 34-43 

Unit  of  Area 13 

"     of  Strain 13 

Upper  Chord  Section 58 

Warren  Truss  or  Single  Triangular 3tJ 


INDEX.  iZ 

f 

PAOH 

Web,  Strains  to '. 82 

"  System 83 

Weights  of  Material 78 

"  "  Plate  Iron 79 

"  ««  Timber,  Table  of 79 

Whipple  Truss,  Single  Canceled 88 

"  "  Double  "  89 

Width  of  Roadway  and  Sidewalks 77 

Wrought  Iron,  Characteristics  of 21 

".  "  Cold-Bend  Test 24 

**  "  Fracture  of 23 

«'  "  ItsRupture 26 

"  •'  Manufacture  of 20 

'«  Testing  of 25 

Zore  or  French  Section  for  Floor  .  ,73 


PART   II. 

SOLUTION  OP  STRAINS  IN  GIRDERS  AND  TRUSSES. 

PAGE 

Action  of  Forces  on  a  Beam 101 

Angle  and  Plate  Iron,  Elastic  Limits 118 

Beams  under  Different  Conditions  of  Loading 105 

Bowstring  Truss,  Illustrative  Example  of  Strains  Solved 140-144 

"  4      Longitudinal  Thrust 139 

"  •*      Strains  in 138 

Breaking  Load 106 

Compound  Girders. 113 

"        Center  of  Gravity,  how  Found 113 

"  "        Horizontal  Increment  in  Web 115 

"  "  "          Strains  in  Flanges 115 

"  "        Rivetingof 115 

Composition  and  Resolution  of  Forces 120 

Compressive  and  Tensile  Strains 102 

Coup'es 103 

Factor  of  Safety 107 

Fink  Suspension  Truss,  Solution  of  Example 138 

"  "      Strainsin. 137 

"  "       on  Suspension  Rods 137 

Flange  Beams. 109 

"    Moment  of  Resistance  of Ill 

Forces  Represented  by  Lines 121 


X  INDEX. 

PAOI 

Formula,  Practical  Application  of 107 

King  Post  Truss,  Strains  in. 122 

Law  of  the  Lever,  Example. 97 

Lever  Arm 100 

Loading,  Different  Conditions  of 109 

Modulus  of  Rupture 104 

Moment  of  Resistance 104 

44       ofRupture 104 

Neutral  Axis 101 

Plate  Girders .* 116 

44          **     Allowance  for  Rivet  Holes 114 

Principle  of  Moments 99 

Queen  Post  Truss,  Counter  Diagonal 125 

"        "       Example  Solved 126 

44         4t        "       Reactions  on  Abutments 127 

44        "        "       Strainsin 124 

Reactions  on  the  Abutments 98 

Rivets,  Duty  of 115 

44        Number  to  be  Used 116 

44        Table  of  Sizes  Proportioned  to  Thickness  of  Web  Plate 118 

44        Value  of 116 

Shearing  Tendency 109 

Strains 121 

Strength  of  Rectangular  Beams 103 

4'         of  Stringers  for  Working  Load 108 

Table  of  Moment  of  Resistance  of  American  Beams 1 12 

44     of  Safe  Center  Load  for  Depths  of  Stringers.  107 

*4     of  Size  of  Stringers  for  Various  Spans 109 

44     of  Web  Strains  Due  to  Movable  and  Fixed  Loads 136 

Triangle  of  Forces 121 

Trusses,  Strains  in 119 

Value  of  a  Rivet  Determined 117 

Warren  Girder,  Chord  Strains 133 

4'  44      Web  Strains,  Dead  Load. 134 

44    .        ««        44          "        Variable  Load 135 

44  4t       Table  of  Strains  on  Diagonals 135 

«4          "     ofWeb  Strains 136 

WebStiffners 117 

Whipple  Truss 127 

"  '4    ChordStrains 128 

"  "        44          "      Example  Solved 129 

"  "    WebStrains 130 

41       4'        4<     Example  Solved 131 

Working  Value  of  Rivets,  Tables  of 118 

Wrought  Iron  Beams,  Co-efficient  of  Safety ..  Ill 


'UNIVERSITY; 


PREFACE. 


IT  will  be  the  effort  of  the  writer  in  the  following 
pages  to  point  out  the  peculiarities  of  material  and  con- 
struction involved  in  the  designing  and  building  of  "  Iron 
Highway  Bridges,"  in  the  hope  that  a  dissemination  of 
their  scientific  principles  in  a  popular  form,  will  bear 
fruit  in  a  more  thorough  appreciation  of  a  noble  art,  and 
in  elevating  the  standard  of  requirements  of  this  very 
important  class  of  public  works.  The  subject  has  been 
divided  into  two  parts,  each  complete  in  itself;  the  one 
general  and  descriptive,  and  the  other  analytical.  The 
former  is  peculiarly  intended  to  present  to  public  com- 
mittees entrusted  with  the  letting  of  bridge  contracts 
such  information  as  they  ought  to  possess,  while  the 
latter  is  offered  as  an  aid  to  engineers  not  experts  in  this 
branch  of  the  profession,  and  yet  who  are  often  called 
upon  to  act  as  inspectors.  The  second  part  develops  the 
strains  in  the  ordinary  forms  of  beams  and  trusses  in  an 
elementary  manner,  the  principle  of  the  lever  being 


8  PREFACE. 

applied  throughout,  to  understand  which  the  simplest 
arithmetical  attainments  are  alone  necessary. 

Great  stress  is  laid  upon  the  "strength  of  joints," 
since  the  essence  of  good  bridge-building  lies  in  their 
proper  design.  A  joint  must  be  as  strong  as  the  parts 
it  serves  to  connect ;  as  in  a  chain,  wherein  a  defective 
link  determines  its  strength,  so  in  a  bridge  the  absence 
of  a  necessary  rivet  would  determine  its  strength.  First- 
class  bridge-builders  recognize  this  relation  as  an  axiom 
ol  their  art,  and  it  is  oftentimes  simply  from  a  conscientious 
application  of  this  vital  principle  that  engineers,  in  mak- 
ing tenders  for  work,  find  themselves  underbid  by 
ignorant  or  unscrupulous  builders,  who  have  no  other  . 
ambition  than  that  of  getting  work.  Ordinarily,  the 
cheapest  proposal  wins  the  day,  simply  because  to  the 
average  committeeman  one  iron  bridge  is  as  good  as 
another,  no  matter  from  what  source  its  plan  emanates. 
To  such  a  man,  difference  in  price  has  no  other  meaning 
than  that  of  being  a  measure  of  the  relative  greed  of  con- 
tractors, and  he  does  not  realize  that  there  exist 
precisely  the  same  reasons  for  large  variations  of  price 
in  iron  bridges  as  for  the  difference  in  price  between  the 
lowest  grades  of  shoddy  and  carefully  woven  goods. 
That  the  wisdom  of  such  a  committeeman  is  evidenced 
by  a  remarkable  freedom  from  bridge  accidents  through- 
out the  country  is  no  defence  for  the  purchase  of  the 


PREFACE.  9 

0 

cheapest  bridge,  simply  because  it  is  a  matter  of  exceed- 
ingly rare  occurrence  that  a  bridge  is  subjected  to  any 
thing  near  the  load  it  ought  to  carry  safely.  The  scat- 
tered travel  of  foot-passengers,  or  the  uncrowded  teams 
on  the  roadway  do  not  test  a  bridge,  and  yet  that  is  the 
usual  condition  of  travel,  particularly  in  country  districts. 
Occasionally,  circumstances  arise  when  a  bridge  may 
become  crowded,  as  was  the  case  at  Dixon,  111.,  when,  on 
a  quiet  Sunday  afternoon,  a  Truesdell  bridge  fell  with  a 
horrible  crash,  killing  and  wounding  many  of  the  citizens 
who  had  congregated  on  that  ill-fated  structure  to  wit- 
ness some  unaccustomed,  and  therefore  crowd-collecting, 
sight.  The  same  story  would  be  repeated  throughout 
the  land,  were  our  ordinary  highway  bridges  subjected 
to  similar  loading ;  and  it  behooves  all  upon  whom  the 
responsibility  of  buying  iron  bridges  rests  to  weigh  well 
that  responsibility,  and  not  to  be  deceived  with  the  idea 
that  their  duty  to  their  constituents  requires  them  to 
erect  the  cheapest  structure  offered.  There  is,  however, 
considerable  difference  in  price  for  good  bridges,  and  a 
good  substantial  bridge  can  be  built  under  any  of  the 
well-recognized  types  of  trusses.  Some  designs  require 
less  material  than  others,  and  the  proportion  of  parts 
relating  to  general  forms,  such  as  depth  of  trusses,  panel 
lengths,  etc.,  still  further  affects  the  amount  of  material 
required.  Two  iron  bridges  may  be  built  on  the  same 


IO  PREFACE. 

general  design,  and  they  may  have  the  same  amount  of 
metal  in  each,  and  yet  one  bridge  is  better  than  the 
other,  just  in  proportion  as  the  workmanship,  the  mate- 
rial, and  design  of  the  joints  are  better.  In  fact,  these 
elements  may  be  so  poor  in  the  second  bridge  as  to 
make  it  positively  unsafe  to  use,  and  yet  to  the  inexperi- 
enced eye  one  bridge  may  seem  almost  the  counterpart 
of  the  other.  If  this  book  does  nothing  more  than 
bring  a  realizing  sense  of  the  above  facts  home  to  those 
public  officers  on  whom  the  responsibility  of  carrying 
out  public  improvements  usually  rests,  the  writer  will 
feel  abundantly  compensated  for  his  labors,  for  he  feels 
well  aware  that  if  this  advance  in  official  sentiment  is 
once  attained,  the  next  step  of  progress  will  certainly 
follow — namely,  the  employment  of  experts  to  prepare 
well-defined  specifications,  and  see  that  they  are  properly 
carried  out. 


OP  THH     ~>£3 

UNIVERSITY 


PART   I. 

GENERAL  AND   DESCRIPTIVE. 

THE  essential  elements  of  a  good  bridge  consist  in  so 
applying  the  materials  of  construction  to  a  given  design 
as  to  have  all  parts  of  the  work  equally  strong  under  the 
maximum  loads  that  can  ever  come  upon  it,  and  that 
a  proper  relation,  called  the  "  factor  of  safety,"  should 
exist  between  the  maximum  loading  and  the  strength  of 
the  structure.  The  term,  factor  of  safety,  as  usually 
applied,  means  the  number  of  times  that  the  maximum 
load  should  be  increased  in  order  to  break  down  a  given 
structure,  a  ratio  that  varies  very  greatly  in  most  Amer- 
ican highway  bridges,  particularly  in  the  "  cheap  ones." 
This  conception  of  the  term,  however,  is  apt  to  be  mis- 
leading, since  it  refers  to  ultimate  strength,  and  not  to 
the  limit  of  effective  strength,  which  last  involves  the 
idea  of  elasticity.  The  elasticity  of  any  material  is  sim- 
ply its  recovering  power  from  the  distortion  produced 
by  the  action  of  a  force,  as  illustrated  in  the  case  of  a 
rubber  ball  under  the  pressure  of  the  hand.  All  mate- 
rials are  more  or  less  elastic,  and  experiments  have 
shown  that  if  this  elasticity  is  not  impaired,  they  are  not 
injured  for  use.  The  strain  at  which  the  recovering 


12  IRON    HIGHWAY    BRIDGES. 

power  of  a  material  is  destroyed  is  called  its  limit  of 
elasticity,  which,  when  once  exceeded,  final  rupture  is 
simply  a  question  of  time.  The  true  measure  of  value, 
therefore,  of  a  material  is  its  elastic  limit,  and  the  real 
factor  of  safety  is  from  one  half  to  one  third  the  values 
employed  when  the  factor  is  referred  to  breaking 
strength,  since  (so  far  as  bridge  material  is  concerned) 
about  that  proportion  exists  between  the  force  necessary 
to  attain  the  elastic  limit  and  that  which  produces  final 
rupture. 

When  we  speak  of  a  factor  of  six,  in  the  ordinary  ac- 
ceptation of  the  term,  it  must  not  be  understood  that  a 
given  structure  can  be  destroyed  only  when  it  is  loaded 
with  six  times  the  load  for  which  it  has  been  propor- 
tioned. While  it  may  not  absolutely  break  down  until  that 
loading  is  reached,  its  value  as  a  structure  is  impaired  the 
moment  the  material  commences  to  be  strained  beyond 
its  elastic  limit,  which  may  be  the  case  with  only  double 
the  extreme  load  which  it  has  been  proportioned  to  car- 
ry. Custom,  however,  has  so  long  made  use  of  this  term, 
"factor  of  safety,"  with  reference  to  ultimate  strength, 
that  in  order  to  avoid  confusion  it  will  be  used  in 
that  sense  throughout  the  following  pages,  and  if  only 
the  preceding  explanation  is  kept  in  view,  it  makes  no 
difference  how  the  factor  is  expressed.  Factors  of 
safety  usually  range  from  four  to  six,  the  most  common 
one  being  five,  and  it  is  good  practice  to  design  a  bridge 
with  two  or  more  factors,  particularly  in  long  spans,  for 
the  reason  that  certain  parts  can  only  be  strained 


FACTOR    OF    SAFETY.  13 

• 

fully  under  the  extreme  conditions  of  loading  (of  very 
rare  occurrence),  while  others  are  brought  under  their 
full  work  almost  daily,  as  can  readily  be  appreciated 
when  the  subject  of  loads  on  bridges  is  considered. 

The  unit  of  intensity  of  a  strain  is  expressed  in 
pounds  or  tons,  and  the  unit  of  area  over  which  a  strain 
acts  is  usually  taken  at  one  square  inch,  and  in  these 
units  of  pounds  or  tons  per  square  inch,  the  factor  of 
safety  is  applied.  It  has  been  before  stated  that  material 
was  uninjured  when  not  strained  beyond  its  elastic  limit, 
and  it  might  seem  at  first  sight  that  the  factor  would  be 
determined  by  dividing  the  ultimate  strength  by  the 
elastic  limit.  Thus  supposing  an  iron  bar  that  took 
60,000  Ibs.  per  square  inch  to  tear  it  apart  lost  its  elas- 
ticity just  beyond  a  strain  of  20,000  Ibs.  per  square  inch, 
the  apparent  factor  that  should  be  used  would  be 

-  =  3,  or,  in   other  words,  the  bar  might  be  sub- 

2OjOOO 

jected  to  a  working  strain  of  20,000  Ibs.  per  square  inch. 
This,  however,  would  be  a  dangerous  practice,  since  an 
allowance  must  be  made  for  the  imperfections  of  work- 
manship and  material  attending  all  human  productions, 
as  well  as  for  endurance  under  the  repeated  application 
of  moving  loads.  This  allowance,  experiment  has  shown, 
should  be  not  less  than  one  third  greater  than  is  expressed 
by  the  ratio  of  the  ultimate  strength  to  the  limit  of  per- 
fect elasticity.  Applying  this  principle  to  the  case  illus- 
trated, the  factor  of  safety  would  become  4  instead  of  3, 
and  the  working  strain  on  the  iron  would  be  15,000  Ibs. 
per  square  inch,  instead  of 


14  IRON    HIGHWAY    BRIDGES. 

THE  LOADS  to  which  bridges  are  subjected,  in  addi- 
tion to  their  own  weight,  are  of  two  kinds  :  that  pro- 
duced by  a  uniform  loading  extending  over  the  whole 
area  of  the  structure,  and  that  produced  by  a  local  con- 
centration of  weight,  such  as  may  be  produced  by  heavy 
stone  and  timber  wagons,  or  the  transport  of  boilers 
and  machinery.  The  effect  of  any  loading  upon  a 
bridge  is  further  dependent  on  the  span,  for  the  longer 
the  span,  the  greater  is  the  fixed  or  dead  weight,  and 
therefore  the  less  is  the  shock  from  passing  loads  felt. 
From  this  it  follows  that  short  spans  should  either  have 
a  higher  factor  of  safety  than  long  spans,  or  else  they 
should  be  proportioned  for  much  heavier  loads.  In 
the  United  States,  short-span  bridges  are  seldom  built 
heavy  enough,  while,  on  the  other  hand,  long-span 
bridges,  say  of  150  feet  and  over,  are  frequently  made 
needlessly  so,  involving  in  consequence  a  useless  ex- 
penditure. 

The  circumstances  of  location  must  be  very  care- 
fully considered,  since  it  is  apparent  that  a  bridge  lo- 
cated in  a  country  district,  subject  simply  to  the  pas- 
sage of  occasional  loads,  can  never  be  strained  like  a 
bridge  in  a  populous  community,  which  may  be  called 
upon  to  bear  the  incessant  traffic  of  a  city,  with  its  pro- 
cessions, and  often  the  reckless  haste  of  a  fire  service. 
Excepting  in  general  terms,  engineers  are  by  no  means 
agreed  as  to  the  exact  loading  for  which  highway 
bridges  under  different  circumstances  should  be  pro- 
portioned. The  usual  standard  is  to  consider  a  span 
crowded  with  people,  which  experiments  have  shown 


LOADING. 


to  vary  within  wicb  limits,  depending  on  the  density 
with  which  a  given  surface  is  packed,  and  the  weight 
of  the  individuals  with  whom  the  experiments  were 
made.  No  probable  contingency,  however,  will  pack  a 
crowd  so  as  to  bring  a  heavier  weight  than  seventy-five 
or  eighty  pounds  per  square  foot  for  a  general  load,  and 
for  local  loads  it  is  well  to  bear  in  mind  that  steam 
road-rollers,  weighing  fifteen  tons  on  an  area  of  sixty 
square  feet,  are  being  introduced  in  many  suburban 
towns,  for  the  compacting  of  Telford  pavement*  The 
following  table,  being  substantially  the  same  as  was  re- 
commended by  a  committee  of  bridge  experts  in  a  re- 
port to  the  American  Society  of  Civil  Engineers,  will 
be  found  useful  in  preparing  specifications  for  road 
bridges,  as  it  gives  a  safe  and  economical  loading  for  all 
circumstances  under  which  bridges  are  usually  built : 


ii. 


in. 


POUNDS  PER  SQUARE  FOOT. 

For     city    and 

For  towns  and 

Ordinary  coun- 

Span. 

other  bridges 
where    travel 

villages,  and 
districts  hav- 

try bridges  — 
travel     infre- 

is heavy  and 

ing  well  -bal- 

quent       ind 

frequent. 

lasted  roads. 

loads  light. 

60  feet  and  under. 

100  Ibs. 

ioo  Ibs. 

75  Ibs. 

60  feet  to  100 

90 

75 

66 

100  feet  to  150 

80 

66 

5° 

150  feet  to  200 

70 

60 

5° 

200  feet  to  300 

66 

5o 

40 

300  feet  to  400 

60 

So 

35 

*  An  Aveling  &  Porter  road-roller  has  fifteen  tons  on  four  wheels  or 
rollers,  each  having  a  width  of  twenty  inches.  A  roller  used  in  England, 
made  by  the  same  parties,  weighs  thirty  tons,  nineteen  of  which  are  on  two 
drivers,  the  width  of  each  driver  being  thirty  inches. 


1 6  IRON    HIGHWAY    BRIDGES. 

The  proper  floor  strength  for  all  spans  may  be  ob- 
tained by  considering  the  loads  on  each  pair  of  wheels, 
for  each  roadway,  and  this  load  on  bridges  of  the  first 
class  may  be  taken  at  from  four  to  five  tons,  on  bridges 
of  the  second  class  three  to  four  tons,  and  on  ordinary 
country  bridges  two  to  three  tons.  This  provision  for 
local  loads  may  seem  extreme  to  many,  but  the  jar 
and  jolt  of  heavy  springless  loads  comes  directly  on  all 
parts  of  the  flooring,  at  successive  intervals,  and  ad- 
monishes us  that  any  errors  made  should  be  on  the  safe 
side. 

From  the  above  consideration  of  local  loads  on 
wheels,  it  follows  that  the  cross  floor-beams  of  a  bridge 
are  required  to  be  of  the  same  size  and  carrying  capa- 
city, whether  close  together  or  far  apart,  being  strained 
alike  in  any  case.  The  longitudinal  stringers,  on  the  other 
hand,  while  increasing  in  size  for  the  same  loads  as  the 
floor-beams  are  spread  farther  and  farther  apart,  are 
independent  of  their  distance  from  each  other.  String- 
ers must  be  of  the  same  strength,  whether  spaced  two 
or  four  feet  apart,  since  any  stringer  may  support  un- 
aided a  wheel  load  midway  between  its  bearings.  If  the 
wheel  loads  are  assumed  to  be  as  high  as  has  just  been 
recommended,  a  factor  of  safety  of  four  will  be  ample  for 
the  floor-beams  and  stringers,  since  the  possibility  of 
such  loads  coming  upon  them  is  very  remote. 


IRON    MANUFACTURE.  I  7 

f 

MATERIALS    OF    CONSTRUCTION. 

In  all  structures  affecting  the  daily  concerns  of  life, 
to  the  strength  of  which  thousands  of  human  beings  in- 
trust their  safety,  the  materials  composing  them  must 
always  be  a  subject  of  deep  interest,  and  therefore  it  is 
of  vital  importance  to  disseminate  as  widely  as  possible 
a  correct  knowledge  of  their  physical  characteristics. 
And  in  this  "  Iron  Age "  upon  which  we  are  enter- 
ing, much  will  be  accomplished  when  the  community 
realizes  that  in  regard  to  iron  at  least,  a  "  little  know- 
ledge is  a  dangerous  thing,"  an  aphorism  applying  with 
peculiar  force  to  bridge-constructions.  The  first  lesson 
to  be  learned  is,  that  iron  is  a  material,  the  qualities  of 
which  are  as  variable  as  the  different  localities  of  its 
production,  and  therefore  that  an  iron  bar  is  not  neces- 
sarily as  good  if  made  in  one  place  as  another,  sim- 
ply because  it  is  iron.  Iron  may  be  very  good  or 
very  bad,  or  it  may  have  all  intermediate  degrees  of 
quality,  and  yet,  to  an  untrained  eye,  a  sample  of  the 
two  extremes  would  seem  to  be  precisely  alike.  It 
must  be  understood  that  iron  is  a  material  the  most 
sensitive  to  treatment  known  in  the  constructive  arts. 
The  least,  and  often  infinitesimal  variation  in  the  fuel, 
ores,  and  working,  will  result  in  many  variations  of 
quality,  and  all  are  more  or  less  useful  for  some  purpose 
or  other.  It  will  be  the  effort  of  the  writer,  in  as  clear 
and  untechnical  language  as  he  can  command,  to  point 
out  the  leading  characteristics  of  this  metal,  particularly 
in  its  application  to  bridge  purposes,  and  he  will  be 


1 8  IRON    HIGHWAY    BRIDGES. 

abundantly  satisfied  if  attention  other  than  professional 
is  awakened  to  the  responsibility  attending  its  selection 
and  use. 

Starting  then  from  the  ore,  which  is  simply  the 
pure  metal  combined  with  different  degrees  of  earthy 
impurities,  we  have,  as  the  first  result  of  the  contact  of 
the  ore  with  the  fuel,  the  product  from  the  blast-fur- 
nace called  pig-iron,  which  commercially  has  different 
grades,  numbered  1,2,  3,  4,  etc.,  all  produced  through 
different  proportions  of  the  fuel  used,  the  tem- 
perature, volume,  and  pressure  of  the  blast  in  a  given 
time. 

The  low  numbers  are  always  the  most  expensive  to 
produce,  and  are  used  for  foundry  purposes,  and  are 
known  as  "  foundry  pig,"  while  the  high  numbers  are 
converted  into  wrought-iron  through  the  medium  of 
the  puddling-furnace,  and  are  called  "  forge-pig."  The 
foundry  irons  are  often  termed  grey  irons,  and  the  forge- 
pig,  white  iron.  Pig-iron  (disregarding  impurities  al- 
ways present)  is  essentially  a  combination  of  carbon 
and  metallic  iron,  which  combination  is  partly  chem- 
ical and  partly  mechanical.  Foundry  pig-iron  may 
be  recognized  by  its  softness,  and,  when  freshly  bro- 
ken, by  its  presenting  a  fracture  of  an  open,  crystal- 
line texture,  and  of  a  dull  grey  color.  Forge-pig  is 
hard  and  fine  grained,  generally  presenting  a  white- 
appearing  fracture,  and  at  other  times  a  mottled  one. 
The  former  flows  readily  in  the  moulds  of  the  foundry, 
being  very  fluid  when  melted,  while  the  latter,  which 


IRON    MANUFACTURE.  19 

f 

melts   at  a  lower  temperature,  is  somewhat  pasty  and 
flows  in  a  sluggish  stream.     The  operation   of  produc- 
ing wrought-iron    is    simply  the    extraction    from  pig- 
iron  of  the  carbon  and  other  impurities,  by  means  of 
the   flame  in  a  reverberatory-furnace,    and  stirring  the 
charge  of  melted  metal  with   iron  bars,  in  order  to  ex- 
pose every  particle  to  the  action  of  the  oxygen  of  the 
air,  which,  combining  with  the  carbon,  passes  off"  up  the 
chimney  as  a  gaseous  product.     The  chemical  operation 
thus  performed  is  called  decarburizing,  which,  were  it 
possible  to  perfectly  accomplish,  and   did  the  pig-iron 
contain    no    impurities,  would   result  in  pure  metallic 
iron,  which  would  be  always  alike  in  quality  and  cha- 
racteristics in  all  parts  of  the  world.     This,  however,  is 
never  the  case,  and  there  results  exceedingly  wide  varia- 
tions in  the  product  of  the  puddling-furnace.     Pig  iron, 
like  its  namesake,  who  would  not  be  driven  to  market, 
must  be  humored,  and  so  metallurgists,  accepting  the 
situation,    have  endeavored  to  regulate  the  quality  of 
their  iron  by  a  judicious  mixture  of  neutralizing  tenden- 
cies.    In  this  they  have  been  entirely  successful,  and  all 
that  an  engineer  has  to  do,  is  to  say  just  what  he  wants 
his  iron  to  withstand,  and  the  service  to  which  it  is  to 
be  put,  and   he  can  have  a  grade  of  metal  proper  for 
such  uses  made  to  order.     As  is  the  quality  of  the  pig- 
iron,  so  is  that  of  the  puddled  product,  which  leaves  the 
furnace  as  a  loose,  spongy-looking  mass,  called  a  "  pud- 
dle-ball," still  impure  with  cinder  and  slag.     The  next 
process  is  to  consolidate  the  ball,  and  force  out  the  im- 


2O  IRON    HIGHWAY    BRIDGES. 

purities  which  are  mechanically  combined  in   the  inter- 
stices of  the  spongy  mass.     This  is  done  by  hammering, 
or  more  usually  by  a  machine  called  a  sneezer,  which, 
as  its  name  implies,  squeezes  out  the  scoriae,  cinder  and 
slag.     The  ball  has  now  taken  another  shape,  bei'ng  con- 
solidated into  an  elongated  mass,  of  such  form  as  to  en- 
able a  still  further  compacting  of  its  particles  through 
the  medium  of  the  first  set  of  rolls,  called  the  roughing- 
rolls,  to  which  the   ball  is  immediately  taken  from  the 
squeezer.     The  iron,  after  being  passed  through  these 
rolls  several  times,  becomes  what  is  called  a  "  paddled 
bar,"  and  in  appearance  looks  like   a  very   rough  and 
jagged-edged   bar  of  flat  iron  about  20  feet  long,  and 
some  4  X  |  inches  in  section.     At  some  mills  these  bars 
are  called  muck-bars.     They  are  then  cut  up  into  short 
lengths,    and    made   up    into  "  piles,"  according  to  the 
shaped  bar  it  is  desired  to  make.     The  piles  are  heated 
in  a  heating-furnace,  and  when  at  a  white  heat  are  taken 
out,  and  passed  back  and  forth  through   the  finishing 
rolls,  from  which  their  marketable  or  commercial  shape 
is  derived.     This  is  called  best  iron,  and  is  the  degree  of 
refinement  sold  by  manufacturers,  when  simply  so  many 
tons  of  iron   are  ordered.     If  made  from  good  stock- 
that  is,  well-selected  pig-iron — such  iron   answers  every 
requirement  for  ordinary  purposes.     But  for  a  bridge,  it 
is  often  required  that  this  best  iron  should  be  again  cut, 
piled,  heated,  and  rolled  into  new  bars,  which  process, 
while  it  does  not  change  the  quality  of  the  iron  in  the 
least,  still  further  refines  it,  and  makes  it  more  uniform 


WROUGHT-IRON.  21 

0 

in  character,  although,  as  may  naturally  be  supposed,  the 
cost  of  the  iron  is  increased  from  ten  to  fifteen  dol- 
lars per  ton.  This  iron  is  known  as  "  Best  Best  "  iron. 
Uniformity  of  material  is  of  very  great  importance  in 
bridge-building — that  is,  if  parties  desire  their  bridges  to 
be  as  strong  in  one  part  as  another ;  and  from  what  has 
preceded,  it  will  be  at  once  seen  that  this  desirable  end 
can  not  be  obtained  by  open  purchases  in  the  market- 
that  is  to  say,  buying  some  bars  here,  and  others  there, 
wherever  the  different  sizes  can  be  obtained  the  cheap- 
est. The  temptation  to  such  a  manner  of  purchasing 
is  great,  in  times  of  close  competition  among  bridge- 
builders,  particularly  when,  in  nine  cases  out  of  ten,  the 
successful  bidder  is  such  simply  from  being  the  lowest 
in  price.  We  come  now  to  speak  of  the  distinctive 
physical  properties  of  iron,  and  firstly  of 

WROUGHT-IRON. 

Take  a  number  of  miscellaneous  bars  of  best  mer- 
chant iron,  fracture  them  short  off,  and  there  will  be  ex- 
hibited probably  as  many  different  appearances  of  the 
fracture  as  there  are  bars.  Some  specimens  will  present 
coarse  crystals,  whitish  in  color,  others  very  fine  ones,  of 
a  dark  gray  appearance,  in  some  lights  almost  black, 
and  in  others  lustrous  like  satin.  Some  specimens, 
again,  may  expose  a  fracture  wherein  coarse  crystals  are 
mingled  with  fine.  Now,  what  does  all  this  express  ?  It 
tells  the  expert  that  one  iron  is  poor  in  quality,  that  it  is 
hard,  brittle,  or  weak,  while  he  reads  the  second  fracture 


22  IRON    HIGHWAY    BRIDGES. 

exactly  the  reverse,  and  as  that  of  an  iron  on  which  de- 
pendence can  be  placed  for  all  purposes  where  strength 
is  required.  The  specimen  showing  a  combination  of 
large  and  small  crystals,  means  that  the  iron  is  not  uni- 
form in  quality,  and  that  it  needed  further  refinement.  A 
fractured  bar  tells  most  every  thing  about  the  quality  of 
iron,  except  that  of  uniformity,  and  it  exhibits  this  at 
times,  as  in  the  case  above  illustrated.  It  so  happened, 
in  the  assumed  exposure  of  fracture,  that  the  bar  was 
broken  at  a  point  where  it  lacked  uniformity,  but  if 
broken  a  few  inches  either  side  of  this  point,  it  might 
not  have  shown  any  coarse  crystals.  Good  iron  that  has 
been  insufficiently  refined  does  not  show  its  lack  of  uni- 
formity throughout  the  whole  length  of  a  given  bar,  but 
in  spots  more  or  less  frequent,  and  it  is  simply  a  matter 
of  chance  if  one  of  these  raw  spots,  as  they  are  some- 
times called,  occurs  at  the  point  of  fracture.  If,  now,  in- 
stead of  breaking  the  bars  off  short,  we  slightly  nick 
them  on  one  side  and  expose  them  to  moderate  blows, 
so  as  not  to  bend  them  too  rapidly,  fibre  will  be  devel- 
oped in  the  iron  of  good  quality,  while  the  poor  coarse 
crystal  iron  may  snap  off  short  again,  after  very  few 
blows.  The  higher  the  quality  of  the  iron,  or  the  nearer 
it  approaches  purity,  the  more  soft  and  silky  will  be  the 
exposed  fibre.  The  phenomenon  of  fibre  can  be  readily 
understood,  when  it  is  remembered  that  all  iron,  whether 
pure,  good,  bad  or  indifferent,  is  built  up,  as  it  were,  from 
crystals,  which  crystals  have  different  degrees  of  fineness, 
depending  upon  impurities  and  the  mechanical  manipu- 


FRACTURE    OF    IRON COLD-BEND    TEST.  23 

0 

lations  during  the  different  stages  of  conversion  from  pig 
iron  to  the  refined  bar.  The  process  of  rolling  develops 
fibre  by  elongating  these  crystals,  so  that  a  bar  of  rolled 
iron  may  be  likened  to  a  bundle  of  metallic  threads  of  dif- 
ferent degrees  of  fineness,  according  to  the  number  of 
times  the  iron  from  which  the  bar  has  been  produced 
has  been  put  through  the  rolls.  It  is  the  ends  of  such 
threads  that  one  observes  when  a  bar  is  suddenly  broken 
off  short,  looking  as  previously  described,  but  when  the 
bar  is  slowly  broken,  the  threads,  having  time  to  arrange 
themselves  in  a  new  position,  draw  out  past  each  other 
and  expose  fibre.  It  follows  from  what  has  preceded 
that  great  judgment  must  be  exercised  in  criticising  the 
quality  of  iron  from  its  fracture,  for  crystalline  fracture 
does  not  in  itself  indicate  poor  iron,  nor  does  a  fibrous 
one  good  iron.  However,  if  care  is  taken  to  fracture 
the  bar  to  be  tested,  under  different  circumstances,  a  fair 
idea  can  be  formed  of  its  quality  and  fitness  for  special 
purposes.  Another  method  of  reading  the  quality  of 
iron  is  known  as  the  cold-bend  test,  which  requires  no 
expert  knowledge  to  understand.  It  consists  in  simply 
bending  unnicked  the  bar  under  examination,  by  repeat- 
ed blows  from  a  heavy  sledge-hammer,  over  the  corner 
of  an  anvil  or  its  equivalent,  until  the  two  sides  approach 
each  other  within  a  distance  equal  to  the  thickness  of 
the  bar.  If  the  iron  stands  this  treatment  without  show- 
ing any  signs  of  fracture  on  the  back  of  the  bend,  it  can 
be  rated  as  of  the  very  best  quality,  possessing  all  the  re- 
quirements for  bridge  purposes — namely,  toughness,  due- 


24  IRON    HIGHWAY    BRIDGES. 

tility,  and  elasticity.  This  test,  of  course,  can  not  show 
uniformity,  that  being  a  matter  depending  on  the  num- 
ber of  workings  as  before  explained,  and  independent 
of  quality.  The  cold-bend  test  is  severer  on  a  square 
bar  than  a  round  one,  inasmuch  as  the  fibres  are  very  ir- 
regularly drawn  out,  being  very  much  strained  at  the 
corners.  Some  very  high-grade  iron  will  even  stand  the 
cold-bend  test  where  a  screw-thread  has  been  cut  upon 
it,  which  is  equivalent  to  numerous  nickings. 

The    annexed    cut    represents   the    appearance  of  a 
flat  and  of  a  round  bar  after  the  cold-bend  test. 


FIG.    1. 

FIG.  2. 


COLD-BEND   TEST. 


It  was  explained,  under  the  head  of  the  Factor 
of  Safety,  that  the  elasticity  of  a  material  was  simply 
its  recovering  power  after  the  removal  of  an  extra- 
neous force,  and  that  so  long  as  the  limit  of  its 
recovering  power  was  not  exceeded,  no  injury  accrued 
to  the  material.  This  limit  of  elasticity  varies  consider- 
ably in  the  different  grades  of  iron,  and  generally  has 
a  value  about  half  the  ultimate  strength  of  the  iron. 
After  the  limit  is  exceeded,  permanent  set  occurs, 
and  the  value  of  the  bar  is  destroyed.  It  is  probable 
that  a  certain  amount  of  permanent  set  takes  place  in 
iron  even  under  the  application  of  very  light  loads,  say 
of  two  or  three  tons  per  square  inch,  but  it  is  so  inap- 


TESTING    OF    IRON STANDARD    QUALITY.  25 

ft 

preciably  small,  being  detected  only  by  the  most  refined 
measurements,  that  it  need  not  be  considered  in  practice. 
The  usual  method  of  testing  a  bar  for  its  elastic  limit, 
is  to  fasten  to  one  end  of  the  testing-machine,  or  to  the  bar 
itself,  close  to  the  point  at  which  it  is  grappled,  a  rod  or  bar 
free  to  move  at  the  other  end,  to  which  free  end  is  attach- 
ed an  index-point.  Before  the  strain  is  applied,  the  test-, 
bar  is  scratched  under  this  index,  which  mark,  after  the  bar 
is  put  under  strain,  will  gradually  move  past  the  stationary 
index,  and  if  the  strain  has  not  exceeded  the  elastic  limit 
of  the  bar  so  soon  as  it  is  removed,  the  mark  will  re- 
turn to  its  former  position  under  the  index.  Successive 
applications  and  removals  of  the  strain  are  required  usu- 
ally to  determine  the  elastic  limit,  else  it  might  be  un- 
wittingly passed  under  a  continually  increasing  power. 
After  becoming  satisfied  as  to  the  elastic  qualities  of  the 
bar,  a  final  application  of  the  strain  can  be  made  in  order 
to  tear  the  bar  in  two,  care  being  taken  to  note  how 
much  it  stretches  before  final  rupture.  This  process  of 
stretching  to  rupture,  exhibits  not  only  the  ductility  of 
the  iron,  but  also  the  degree  of  uniformity,  shown  by  a 
greater  or  less  inequality  in  the  amount  of  stretching  at 
different  portions  of  the  bar. 

The  beauty  of  the  cold-bend  test  is,  that  it  shows  simply 
and  inexpensively  the  same  qualities  (excepting  unifor- 
mity) that  the  testing  apparatus  measures  in  pounds  and 
inches,  and  for  practical  purposes  nothing  else  is  needed. 
The  result  of  many  thousands  of  experiments  on  Am- 
erican irons  shows  that  for  bridge  purposes,  bar-iron 


26  IRON    HIGHWAY    BRIDGES. 

should  stand  at  least  50,000  Ibs.  per  square  inch  before 
rupture,  should  have  an  elastic  limit  not  less  than  20,000 
Ibs.  per  square  inch,  and  should  elongate  at  least  twelve 
per  cent  of  its  length  (or  i^  inches  to  the  foot),  before 
ultimate  strength  is  reached.*  Most  of  the  first-class 
bridge-builders  use  a  higher  grade  iron  than  the  above, 
which  is  given  simply  as  a  minimum  quality  for  high- 
way-bridges, easily  attainable.  Angle-iron  and  plate- 
iron,  as  usually  applied,  are  from  ten  to  fifteen  per  cent 
weaker  than  good  bars,  and,  therefore,  bridges  built  from 
such  irons  should  have  proportionately  just  so  much 
excess  of  metal  over  bridges  built  from  bars,  a  require- 
ment that  the  buyers  of  iron  bridges,  in  this  country  at 
least,  have  not  as  yet  learned  to  insist  upon.  Before 
passing  from  this  subject,  it  should  be  remarked  that  the 
tables  of  strength  of  wrought-iron  are  based  upon  exper- 
iments made  on  small  bars,  having  cross-sectional  areas 
of  about  one  inch.  Large  bars  will  not  show  the  same 
ultimate  strength  that  small  ones  do,  of  the  same  make, 
a  fact  that  must  be  borne  in  mind  when  specifications 
are  being  prepared.  For  example,  the  same  iron  in  a 
bar  having  one  inch  area  may  require  a  strain  equiva- 
lent to  10,000  Ibs.  per  square  inch  to  rupture  it,  in  excess 
of  that  required  when  formed  in  a  bar  having  an  area 
of  four  or  five  inches.  Until  a  comparatively  recent  date, 
no  attention  was  paid  to  the  effect  of  the  form  of  the 
specimen  to  be  tested.  Test  specimens  are  simply  short 
pieces  of  iron,  three  or  more  inches  long,  the  middle  of 
which  is  grooved  down  to  exact  gauge,  and  which  be- 

*  Very  accurate  gauging  under  a  magnifying  instrument  will  indicate  a  per- 
manent set  long  before  20,000  Ibs.  per  square  inch  is  reached,  and  probably 


TEST    SPECIMENS CAST-IRON. 


FIG.  2. 


FIG.   I. 


comes  the  area  to  which  the  breaking  strain  is  referred. 
The  character  of  the  grooving,  whether  long  or  short, 
affects,  in    a    marked    degree,  the  result  of  a  test.     If 
the    groove    is    a  short  one,  the  iron  will  break   at  a 
much  higher  strain  per  square  inch  than  if  it  had  been 
long,  and  this  result  is  due  to  the  fact  that  a  free  stretch- 
ing of  the  fibres  is  prevented  by  the  reinforcement  de- 
rived from  the  metal  contiguous  to  the  ruptured  section 
of   the  short-grooved   specimen.      This   difference,  due 
solely  to  the  preparation  of  the  specimen,  will  amount 
in  some  cases  to  as  much  as  fifty  per  cent.     The  expla- 
nation of  this  apparent  anomaly  in  the  strength  of  iron 
may   be  made  still  clearer  by    an  in- 
spection  of  the  cut,  where  Fig.  i    re- 
presents a  long-grooved  specimen,  and 
Fig.  2  a  short-grooved  one.  The  shoul- 
ders at  either  end  are   formed   for  the 
grappling-irons  of  the  testing-machine. 
There    are   two  terms    continually 
met  with  among  iron-workers — name- 
ly, red-short  and  cold-short  iron,  which 
it  may  be  advisable  to  explain.     The 
peculiarity    of    the     former     is,    that 
while   very    strong    and    tough    when 
cold,  it  is  difficult  to  work   in  the  forge  except  under 
very  high  heats,  otherwise  it  will  crumble   and  waste, 
and  for  this  cause  has  received  the  enmity  of  smiths. 
On  the  other  hand,  cold-short  iron  is  brittle  when  cold, 
and  absolutely  unsafe  to  use  where  life  depends  upon  its 

with  not  over  a  ton  strain — but  ordinary  methods,  such  as  are  used  in  the  shops, 
will  not  detect  a  set  below  20,000  to  25,000  Ibs.  per  square  inch. 


SHORT   AND    LONG 
GROOVED    SPECIMENS. 


28  JRON    HIGHWAY    BRIDGES. 

integrity.  The  smith  likes  to  use  it,  since  it  works  and 
welds  readily  in  the  forge  at  low  heats.  The  best  manu- 
facturers aim  to  have  a  neutral  product,  which,  if  it  has 
any  tendency  at  all,  is  on  the  side  of  red  shortness. 

Cast-iron  in  bridge-building  is  so  little  used  at  the 
present  day,  except  in  the  form  of  bearing-blocks,  poet- 
caps  and  bases,  or  washers,  that  little  need  be  said  about 
it.  In  its  very  nature,  it  is  a  brittle  material,  and  even 
while  apparently  doing  good  service,  may  be  dangerous- 
ly near  failure.  It  has  an  irregular  elasticity,  and  in  cold 
climates  it  has  been  known  to  fracture  through  the 
freezing  of  water  that  had  found  its  way  into  unpro- 
tected cavities.  In  the  form  of  long  columns,  it  is  of 
course  very  inferior  to  wrought-iron.  Such  columns  are 
exposed  to  cross  strains,  and  have  a  tendency  to  fail  by 
bending  and  not  by  crushing.  Tension  in  some  part 
always  accompanies  a  cross  strain,  to  resist  which  cast- 
iron  is  a  very  uncertain  material.  Castings  may  have 
initial  strains  through  unequal  cooling,  or  they  may  be 
thinner  on  one  side  than  another,  or  they  may  be  weak 
through  concealed  holes,  "  cold  shuts,"  or  cinder.  No 
human  foresight  can  remove  these  risks ;  and  especially 
in  bridge-building  is  it  important  to  reduce  all  risks  to  a 
minimum,  and  for  this  reason,  if  for  no  other,  cast-iron 
should  be  discarded  for  such  purposes,  except  in  those 
places  where  it  would  be  very  expensive  to  forge  wrought- 
iron,  places  where  none  other  than  a  direct  crushing 
strain  can  ever  occur,  as  previously  instanced.  The  iron 
from  which  castings  are  made  should  be  selected  with 


TIMBER.  29 

f 

great  care,  and  it  should  have  sufficient  meltings,  2  to  4, 
before  being  put  into  its  final  shape.  Such  castings, 
when  broken,  should  present  a  fine-grained  grayish  frac- 
ture, and  their  skin  should  be  generally  smooth,  but  not 
smooth  like  stove-plate  castings,  as  such  iron  is  very  un- 
suitable where  strength  is  desired.  Stove-plate  cast- 
ings must  be  made  from  a  very  fluid  iron,  one  that  runs 
thin,  and  sharply  fills  the  moulds,  and  such  irons  are 
very  weak.  Ordnance  iron,  with  a  tensile  strength  oc- 
casionally equal  to  that  of  inferior  wrought-iron,  is  the 
best  cast-iron  possible  to  have,  but  it  is  expensive,  and 
rarely  used  on  that  account.  Such  a  grade  of  iron,  how- 
ever, should  always  be  insisted  upon  where  bridges  are 
permitted  to  be  built  having  cast-iron  top  chords  and 
posts. 

TIMBER. 

Whatever  modesty  is  shown  through  conscious 
ignorance  in  criticising  iron  and  its  fabrication,  it 
quickly  disappears  when  the  question  of  timber  is  un- 
der consideration,  almost  every  one  being  positive  as  to 
what  is  good  timber,  and  very  frequently  unreasonable 
exactions  are  imposed.  The  main  trouble  that  arises,  in 
the  execution  of  contracts,  arises  from  the  interpretation 
given  to  the  term  merchantable,  an  expression  some- 
what vague,  without  other  limitations.  All  bridge-timber 
should  be  sound — that  is,  free  from  loose  or  black  knots, 
heart-cracks,  and  wind-shakes,  and  it  should  not  be  cut 
from  logs  obtained  from  dead  trees.  Seasoned  timber, 


30  IRON    HIGHWAY    BRIDGES. 

especially  when  it  has  been  exposed  to  the  direct  rays  of 
the  sun  during  the  process  of  seasoning,  is  apt  to  have 
more  or  less  cracks,  called  season-cracks,  which  must  not 
be  confounded  with  heart-cracks  and  shakes.  They  can 
be  distinguished  from  each  other  from  the  fact  that  the 
cracks  due  to  seasoning  are  sharp,  while  those  due  to 
shakes  are  splintery — the  splinters,  in  many  cases,  being 
easily  torn  off.  Well-seasoned  timber  wears  much 
longer  than  green  timber ;  but  since  bridge-plank  is 
seldom,  if  ever,  kept  in  stock,  and  since  public  works 
rarely  have  their  needs  anticipated,  lumber  is  almost  al- 
ways procured  fresh  from  the  mills.  The  durability  of 
timber  would  be  very  much  enhanced  if  kept  soaking  in 
water  for  a  few  months  after  it  is  cut  into  plank, 
after  which  seasoning  proceeds  very  rapidly,  the  water 
having  acted  as  a  solvent  in  ridding  the  pores,  to  a  great 
extent,  of  sap  and  nitrogeneous  matter,  the  decaying 
elements  of  wood.  Sap-wood — that  is,  the  wood  newest 
made  and  next  the  bark — is  not  desirable,  as  it  will  wear 
away  faster  and  decay  sooner  than  the  heart-wood,  but 
practically  it  is  impossible  to  obtain  timber  of  any  size 
and  in  large  quantities  entirely  free  from  it,  unless  at  a 
very  great  increase  of  cost.  Sap-wood  may  be  recog- 
nized as  being  lighter  in  color,  softer,  and  of  more  open 
fibre  than  the  heart-wood.  Timber  is  regarded  as  mer- 
chantable when  it  has  not  more  than  three  sappy  cor- 
ners, although  some  inspectors  do  not  permit  of  more 
than  two ;  but  as  bridge-plank  usually  wear  out  before 
they  rot  out,  a  latitude  can  with  propriety  be  observed 


CLASSIFICATION    OF    BRIDGES.  3! 

• 

here,  and  the  plank  laid  with  the  sap  corners  down, 
thus :  1  the  dark  portion  representing  the 

sap-wood.  Wane  or  bark  edges  are  very  apt  to  occur 
in  otherwise  first-class  sound  timber,  but  should  not  in- 
sure condemnation  if  only  on  one  corner,  if  the  plank  can 
be  laid  with  that  corner  down.  If  on  two  under  corners, 
the  plank  would  be  next  to  the  slab  (or  outside  cut), 
and  therefore  almost  all  sap-wood,  and  should  not  be 
permitted  to  pass  by  the  inspector.  For  stringer  tim- 
bers, inspection  ought  to  be  somewhat  more  rigid  than 
for  floor-plank,  but  guided  by  the  same  common-sense 
principles,  and  the  farther  consideration,  how  much  sur- 
plus strength  the  stringers  possess.  The  kinds  of  lum- 
ber used  are  mostly  oak  and  pine,  both  white  and  yel- 
low ;  to  these  may  be  added,  for  plank  purposes,  beech, 
birch,  and  maple,  and  occasionally  spruce,  when  two 
courses  of  plank  are  used,  the  upper  one  being  of  hard 
wood.  All  things  being  considered,  the  writer  prefers 
close-grained  yellow  pine  for  floor-planks,  it  being  much 
less  expensive  than  a  proper  quality  of  oak,  and  besides 
less  slippery  for  horses  in  frosty  weather.  As  to  artifi- 
cial means  for  preserving  timber,  a  number  of  processes 
have  been  tried  with  success.  The  various  methods  of 
creosoting  and  burnetizing  are  the  more  common  in  use. 
The  city  of  Boston  required  the  latter  process  to  be 
applied  to  spruce  plank  in  some  bridges  recently  built, 
as  one  eminently  effective  and  cheap.  Any  process 
used,  unless  thoroughly  well  done — that  is,  unless  all  the 
pores  and  cells  vxt  filled  with  the  preservative  material — is 


32  IRON    HIGHWAY    BRIDGES. 

even  detrimental,  since  in  such  cases  dry  rot  inevitably 
sets  in  at  an  early  day. 

KINDS    OF    BRIDGES. 

The  various  kinds  of  bridges  ordinarily  met  with 
may  be  classed  under  one  of  four  heads,  namely,  the 
plain  beam  or  girder,  the  beam  truss,  the  suspension 
truss,  and  the  arch  truss  or  bowstring.  The  first  class 
needs  no  explanation.  The  second  form  includes  all 
trusses  where  both  top  and  bottom  chords  are  absolutely 
essential,  while  the  third  embraces  those  trusses  wherein 
only  the  upper  chord  is  essential.  The  bowstring  is  pro- 
perly not  a  truss  at  all,  but  simply  an  arch  wherein  the 
horizontal  tie  takes  the  place  of  fixed  abutments.  The 
office  of  all  girders,  whether  plain  or  trussed,  is  to  trans- 
mit weight  to  the  points  of  support,  which  action  de- 
velops two  classes  of  strains,  namely,  horizontal  and 
vertical  (sometimes  called  shearing).  The  former  are 
resisted  by  the  top  and  bottom  longitudinal  chords 
or  flanges,  while  the  latter  are  taken  up  by  the  interme- 
diate bracing,  called  collectively  the  web,  which  applies 
to  all  the  material  lying  between  the  chords  or  flanges, 
whether  open  as  in  a  truss,  or  solid  as  in  a  plate-girder. 
The  longitudinal  strains  in  the  chords  are  either  com- 
pressive  or  tensile,  and  whichever  may  be  the  case,  the 
quality  of  the  strain  is  the  same  throughout  the  chord 
considered.  The  web  is  exposed  to  both  kinds  of  strain, 
the  parts  of  which,  if  a  truss,  are  alternately  in  tension 
and  compression  in  the  march  of  a  given  weight  to 


WEB    SYSTEM. 


33 


either  abutment.  The  tension  members  of  the  web  are 
called  ties,  and  they  may  be  either  vertical  or  inclined. 
The  compressive  portions  of  the  web  are  called  struts, 
or  posts,  and  may  also  be  vertical  or  inclined.  When 
ties  are  vertical,  the  posts  are  inclined,  and  vice  versa*  or 
both  may  be  inclined.  Strut  tie,  as  the  name  implies, 
means  that  a  web  member  may  act  either  by  tension  or 
compression.  The  point  where  a  tie  and  a  strut  intersect 
in  a  chord,  is  called  a  panel-point,  and  the  distance 
between  two  such  points  is  called  a  panel-length.  Again, 
a  portion  of  the  web  system  are  called  main  braces,  or 
ties,  and  a  portion  counter  braces,  or  ties.  The  former 
embrace  all  parts  of  the  web  which  carry  that  part  of  the 
weight  going  to  the  nearer  abutment  either  side  of  the 
centre  of  the  truss,  and  are  lightest  toward  the  middle 
and  heaviest  toward  the  ends  of  the  span,  while  the  lat- 
ter run  in  a  contrary  direction  to  that  of  the  main  braces, 
and  carry  that  portion  of  the  load  going  to  the  farther 
abutment,  and  they  are  heaviest  at  the  centre  and  least 
at  the  ends  of  the  span.  Main  braces  may  be  made  to 
act  as  counters,  if  they  are  constructed  to  act  either  by 
tension  or  compression.  The  office  of  the  "  counters  "  is 
simply  to  prevent  distortion  or  change  of  form  in  a  truss, 
and  they  are  only  necessary  when  the  truss  is  subjected 
to  the  action  of  a  variable  load,  as  is  the  case  on  all 
bridges.  They  can  only  act  when  the  main  braces  to 
which  they  are  opposed  are  relaxed,  and  then  have  an 
action  equal  to  the  difference  between  the  effects  of 
the  variable  and  fixed  loads,  acting  in  opposite  direc- 


34  IRON    HIGHWAY    BRIDGES. 

tions.  In  a  bridge  very  heavy  in  proportion  to  the 
moving  load,  this  excess  is  soon  lost  either  side  of  the 
truss  centre,  when  the  counters  can  of  course  be  left  out. 
Ordinarily  they  are  continued  a  short  distance  beyond 
theoretical  requirements,  in  order  to  diminish  vibration, 
which  they  materially  assist  in  preventing  when  screwed 
up  tightly.  The  usual  forms  of  truss  bridges  are  illus- 
trated by  the  succeeding  figures,  on  each  of  which  is  re- 
presented, by  means  of  lines  of  varying  width,  not  only 
the  parts  strained  the  greatest,  but  also  the  kind  of 
strain.  Tension  is  shown  in  fine  lines,  and  compression 
in  full  black  ones.  The  weights  producing  strain  are 
supposed  to  be  located  immediately  at  the  panel-points, 
the  whole  materially  aiding  the  mind  in  forming  a  very 
fair  idea  of  how  trusses  really  do  act,  when  coupled  with 
the  descriptions  and  definitions  just  given. 

Figs.  3  and  4  represent  plain  girders  for  short  spans, 
in  which  the  flange  and  web  parts  are  noted.     Such  gir- 


WEB  OR  STEM.        ^^H^ ,,,f^&  WEB  OR  STEM. 


FIG.    3.    SOLID    ROLLED  BEAM.  FIG.    4.    COMPOUND  RIVETED  GIRDER. 

ders  are  often  used  of  solid  section,  and  are  called  rolled 
beams,  being  finished  ready  for  use  direct  from  the  rolling- 
mills.  They  are  made  of  varying  sizes  and  weights,  from 
the  four-inch  beam,  weighing  30  Ibs.  per  yard,  to  the 


KING    AND    QUEEN    POST    TRUSSES.  35 

9 

fifteen-inch  beam,  weighing  200  Ibs.  per  yard.  These 
beams,  however,  are  more  expensive  than  the  compound 
riveted  girder,  made  with  plates  and  angle  irons,  but  are 
10  per  cent  stronger.  The  riveted  girder  can  be  made 
of  any  depth,  and  is  therefore  adapted  for  much  longer 
spans  than  the  rolled  beams. 

Fig.  5  shows  the  simplest  form  of  truss,   and  con- 
sists of  a  post  and  two  inclined 

t. 
ties  supporting  the  middle  of  a 

beam,  that  would    otherwise    be 
too  weak  to  sustain  a  load.     This 
supporting  system  in  effect  halves 
the    span,   the    post    performing     FIG.  5.  KING  POST  TRUSS. 
the   office    of    a    pier,    carrying 

one  half  the  load  of  both  subdivisions  of  the  beam. 
Now,  since  all  the  load  must  finally  rest  on  the  two  end 
supports  or  abutments,  that  portion  that  rests  on  the 
post  can  only  reach  them  through  the  medium  of  the 
inclined  ties,  intersecting  at  its  foot,  each  tie  taking  up 
half  the  load  carried  by  the  post.  These  ties  are  strained 
in  excess  of  the  load  they  transmit  to  the  abutments  in 
proportion  to  their  deviation  from  a  vertical  line  ;  or,  in 
other  words,  an  inclined  pull  requires  greater  effort  than 
a  direct  one,  as  almost  eveiy  one  has  experienced. 
Whenever  a  force  is  exerted  at  an  angle,  a  horizontal 
effect  is  always  produced,  and  in  proportion  to  the  angle 
at  which  it  is  applied.  The  flatter  the  angle,  the  greater 
the  horizontal  effect,  and  vice  versa.  In  the  truss  before 
us,  the  abutment  ends  of  the  inclined  ties,  by  virtue  of 


36  IRON    HIGHWAY    BRIDGES. 

this  horizontal  effect,  pull  toward  each  other,  producing 
compression  in  the  horizontal  beam  to  which  they  are 
attached.  This  form  of  truss  is  called  the  "  King  Post  " 
truss,  and  when  inverted  will  be  at  once  recognized  as 
the  commonest  form  of  wooden  trussing  in  existence. 
In  that  case,  however,  the  vertical  post  becomes  a  tie, 
the  inclined  ties  become  thrust  braces,  and  the 
beam  is  strained  tensively,  instead  of  compressively, 
since  the  horizontal  effect  of  the  inclined  thrust  braces 
is  to  tear  the  beam  apart. 

Fig.  6.  When  an  opening  becomes  too  great  to   be 
spanned  by  a  beam  trussed  with  a  single  post,  two  posts 


FIG.   6.   QUEEN   POST   TRUSS. 

are  added,  forming  three  spans,  the  posts  being  the 
piers  as  before,  which  piers  are  supported  in  turn  by  the 
inclined  ties  running  up  to  the  ends  of  the  horizontal 
beam  as  before ;  each  tie  sustaining  the  whole  weight 
on  one  pier  or  post.  This  is  a  complete  truss  when 
both  posts  are  loaded  ;  but  if  only  one  is  loaded,  the 
condition  of  affairs  changes.  The  load  is  unbalanced 
on  the  other  side  of  the  centre,  and  the  horizontal  ef- 
fect of  the  inclined  tie  on  the  loaded  side  will  be 
greater  on  the  beam  (which  hereafter  we  will  call  the 


KING    AND    QUEEN    POST    TRUSSES.  37 

0 

upper  chord)  than  that  from  the  similar  tie  on  the  un- 
loaded side.  The  result  will  be  a  distortion  of  the 
frame,  the  loaded  post  sinking  and  the  unloaded  one 
rising.  All  that  is  necessary  to  prevent  this  destruc- 
tive effect,  is  to  enable  that  portion  of  the  load  that 
must  be  carried  by  the  further  abutment,  to  go  there 
by  the  most  direct  route,  which  is  manifestly  through 
the  medium  of  a  diagonal  tie  from  the  foot  of  the 
loaded  post  to  the  top  of  the  unloaded  one,  or  a  diago- 
nal strut  from  the  top  of  the  loaded  post  to  the  foot  of 
the  unloaded  one.  This  diagonal  is  the  counter-diago- 
nal previously  defined.  Its  introduction  in  the  elemen- 
tary truss  just  described,  and  known  as  the  "  Queen 
Post  Truss,"  is  a  pointed  illustration  of  the  value  of  the 
triangle  in  trussing,  which  is  the  only  geometrical 
figure  that  resists  change  of  form.  Inverting  this  truss, 
as  was  done  before  with  the  King  Post,  we  have  the 
Queen  Post  in  a  more  familiar  shape ;  and  while  the 
effect  of  the  loads  on  the  several  parts  is  pre- 
cisely the  same  in  amount  of  strain  engendered,  the 
quality  is  reversed.  That  is,  the  upper  chord  be- 
comes now  the  lower  chord,  and  suffers  tension, 
the  inclined  ties  become  thrust  braces,  the  posts 
change  to  ties,  and  the  lower  chord  beconies  now  the 
top  chord  undergoing  compression.  The  counter- 
diagonals  also  become  reversed  as  to  tension  or  com- 
pression. 

The  forms  of  trusses  just  described  embrace  all  the 
elements  of  simple  trussing,  and  an  extension  of  these 


IRON    HIGHWAY    BRIDGES. 


principles  is  all  that  is  necessary  to  meet  the  ordinary 
requirements  of  every-day  practice.  By  adding  to  the 
number  of  posts,  the  Whipple  or  Pratt  truss,  Figs.  7  and  8, 


FIG.    7. 


FIG. 


WHIPPLE    SINGLE   CANCELLED   TRUSSES. 


is  formed,  a  plan  of  truss  the  popularity  of  which  is  well 
deserved.  The  inclination  of  the  end  posts,  though  not 
essential,  results  in  a  saving  of  material  over  vertical 
posts,  but  the  latter  form  produces,  in  the  judgment  of 
many,  a  more  pleasing  effect.  A  study  of  the  diagram 
will  show  how  cumulative  the  horizontal  effects  of  each 
diagonal  main  tie  are  toward  the  centre  of  the  chords ; 
and  also  how  it  is  that  any  main  tie  must  carry  all  the 
weight  between  its  own  panel  load  and  the  centre  of  the 
span. 

Fig.  9.  When  a  span  becomes  very  long,  and  it  is 
constructively  and  economically  inconvenient  to  have 


WHIFFLE    AND    WARREN    TRUSSES. 


39 


one  system  of  triangles,  two    systems    are    introduced, 
complete  and  independent  of  each  other,  each  one  being 


FIG.    9.   DOUBLE   CANCELLED   WHIPPLE  TRUSS. 

formed  of  triangles  having  bases  of  two  panel-lengths. 
The  principle  of  the  Queen  Post  still  holds  good  as  be- 
fore, as  it  would  do  if  there  were  three  or  more  series  of 
triangles,  each  series  doing  its  own  work  in  transmitting 
the  loads  to  the  abutments,  independent  of  any  other. 
The  truss  illustrated  in  Fig.  9  is  known  as  the  double 
cancelled  Whipple  or  Quadrangular  truss,  and  has  been 
used  in  spans  of  over  400  feet. 

Fig.   10   appears,  at    first  sight,  a   greater  variation 
from   the    elementary  truss   form    previously  described 


AAAAA 


FIG.    10.   SINGLE  TRIANGULAR   OR  WARREN   TRUSS. 

than  is  really  the  case.     The  principle  of  the  triangle 
being  here  developed  to  its  utmost  perfection,  this  form 


4O  IRON    HIGHWAY    BRIDGES. 

is  usually  known  as  the  "  Triangular  "  truss,  although 
sometimes  called  the  "  Warren  Girder."  The  marked 
difference  between  this  form  of  truss  and  the  Whipple 
and  Queen  Post  trusses  consists  in  the  fact  that  the 
posts  as  well  as  the  tension-rods  are  inclined,  and  if  the 
angle  of  inclination  is  well  proportioned,  a  considerable 
economy  of  material  is  obtained  over  that  required  by 
the  straight  post  trusses.  When  a  vertical  post  is  used, 
the  weight  delivered  to  it  by  its  tension-rod  makes  no 
progress  whatever  toward  the  abutment ;  but  in  the  case 
of  an  inclined  post,  by  the  time  the  weight  has  been 
transmitted  to  its  foot,  it  has  progressed  toward  the 
abutment  by  an  amount  equal  to  the  horizontal  reach 
of  the  post.  When  the  span  becomes  long  and  the 
stretch  of  the  triangles  is  so  great  as  to  necessitate  an 
intermediate  support  for  the  flooring,  a  rod  is  dropped 
from  the  apexes  of  the  triangles  to  form  such  support, 


FIG.    II.   DOUBLE  TRIANGULAR   OR  LATTICE  TRUSS. 

or  two  systems  of  triangles  may  be  used  corresponding  to 
the  double  cancelled  Whipple  truss,  as  in  Fig.  1 1.  In  the 
case  of  the  trusses  being  beneath  the  roadway,  the  verti- 


FINK    SUSPENSION    TRUSS.  4! 

• 

cal  rod  becomes  a  post,  as  the  load  then  presses  from 
above,  instead  of  being  suspended  from  below.  In  this 
form  of  truss,  it  will  be  noticed  that  the  horizontal  ef- 
fect at  each  panel-point  is  made  up  of  two  portions — one 
due  to  the  thrust  of  the  posts,  and  the  other  to  the  pull 
of  the  ties,  both  being  inclined  and  acting  in  the 
same  direction — just  as  a  man  pushing  behind  a  wagon 
adds  to  the  effect  of  a  man  pulling  it  in  front.  While 
the  vertical  post  truss  has  only  one  increment  at  each 
panel-point,  yet  for  the  same  depth  of  truss  the  sum  of 
all  the  increments  on  either  system  will  be  the  same  at 
the  centre  of  the  chords. 

Fig.  1 2  illustrates  the  suspension  truss,  where  only 
a  top  chord  is  essential,  and   is  nothing  more  than  an 


FIG.    12.    FINK    SUSPENSION   TRUSS. 


ordinary  roof  truss  turned  upside  down.  This  form 
was  first  developed  for  bridge  purposes  by  Mr.  Albert 
Fink,  and  it  almost  universally  goes  by  his  name.  It  is 
developed  from  the  elementary  truss,  Fig.  5,  as  will  be 
apparent  on  inspection.  By  imagining  the  King  Post 
truss  in  Fig.  5  to  become  so  long  as  to  require  inter- 
mediate support,  it  is  accomplished  in  this  case  by  add- 
ing sub-systems,  acting  precisely  like  the  main  system, 


42  IRON    HIGHWAY    BRIDGES. 

only  in  a  minor  degree.  The  load  on  each  post  splits 
in  half,  as  it  were,  at  the  post-foot,  each  portion  being 
carried  up  the  inclined  ties  to  the  top  of  the  adjoining 
posts,  each  minor  system  thus  adding  to  the  weight  im- 
posed on  the  next  larger  system,  until  the  whole  load  is 
finally  delivered  to  the  abutment.  The  main  system  ex- 
tending over  the  whole  span  is  called  the  primary  sys- 
tem ;  the  systems  extending  over  each  half  span  are 
secondary  systems ;  those  over  each  quarter  of  the  span, 
are  tertiary  systems ;  those  over  each  eighth  of  the  span, 
quaternary  systems,  and  so  on.  The  horizontal  incre- 
ments of  all  the  ties  accumulate  at  the  extreme  ends  of 
the  top  chord,  producing  uniform  compression  through- 
out its  whole  length. 

Fig.  13  is  the  familiar  bowstring,  which  acts,  as  be- 
fore remarked,  like  an  arch,  and  bears  no  relation  what- 


FIG.    13.    BOWSTRING  TRUSS. 

ever  to  the  typical  form  of  trusses  developed  from  Figs. 
5  to  12.  The  essential  parts  are  the  bow  and  tie,  the 
latter  taking  the  place  of  fixed  thrust  abutments.  The 
web  for  a  uniform  load  need  be  nothing  more  than  ver- 
tical rods,  carrying  simply  the  separate  loads  at  the 
panel-points.  Where  the  load  is  variable,  as  is  always 


THE    SELECTION    OF    BRIDGES.  43 


. 


the  case  in  bridges,  and  if  the  arch  is  not  stiff  enough  in 
itself  to  resist  distortion,  diagonals  must  be  introduced 
in  the  web  performing  simply  the  office  of  counter- 
braces.  Like  them,  they  are  strained  the  greatest  in  the 
centre  of  the  span  and  least  at  the  ends. 

THE    SELECTION   OF    BRIDGES 

should  be  governed  by  economy  and  adaptability  to  lo- 
cation, since  no  one  of  the  well-recognized  types  of 
bridges  is  better  than  another.  Apart  from  such  mo- 
tives, any  bridge  designed  on  correct  principles  is  a 
good  one,  whether  a  beam-truss,  a  suspension-truss,  or  a 
bowstring.  On  the  contrary,  any  one  is  bad  if  impro- 
perly designed,  and  the  principles  of  its  construction 
ignorantly  conceived.  A  general  rule  that  will  lead  to 
satisfactory  results  is  to  ignore  any  plan  of  bridge  that 
can  not  be  accurately  analyzed  as  to  the  character  and 
amoimt  of  strain  occurring  in  all  its  parts — such,  for 
instance,  as  the  Truesdell  bridge,  scores  of  which  have 
been  built  during  the  last  fifteen  years ;  and  assuming 
that  the  great  majority  are  still  in  use,  giving  satisfac- 
tion to  their  users,  yet  their  form  of  construction  is  one 
that  removes  them  beyond  the  pale  of  the  most  refined 
analysis.  They  are  purely  empirical  structures,  and  be- 
ing such  their  construction  should  under  no  circum- 
stances be  permitted.  It  is  bordering  on  criminality  to 
build  any  structure  on  a  plan  that  no  human  being  can 
tell  definitely  any  thing  about,  when  there  are  so  many 
plans  that  we  thoroughly  understand. 


44  IRON    HIGHWAY    BRIDGES. 


METHODS   OF   CONSTRUCTION   AND 
FORMS    OF   SECTIONS. 

The  various  systems  under  which  iron-work  is 
framed  may  be  classified  as  the  "  pin  connection," 
"  screw-end  connections,"  and  all  "  riveted  connections," 
which  may  be  and  often  are  combined,  to  a  greater  or 
less  extent,  in  the  same  bridge.  The  first  two  systems 
are  peculiarly  American  in  their  origin  and  practice, 
while  the  last  is  the  system  pursued  almost  entirely  in 
England  and  on  the  Continent,  although  latterly  the  at- 
tention of  American  engineers  has  been  drawn  to  a  con- 
siderable extent  to  riveted  work.  As  has  been  before 
intimated,  the  knowledge  of  a  good  bridge-designer 
will  be  shown  in  his  details,  more  than  in  his  mathe- 
matical expertness  in  figuring  up  strains  ;  and,  perhaps, 
it  will  not  be  hazarding  too  much  to  say,  by  way  of 
emphasizing  this  remark,  that  few  iron  highway  bridges 
built  in  the  United  States  are  as  strong  at  the  joints  as 
the  parts  they  serve  to  connect.  The  very  great  diffi- 
culty in  obtaining  this  joint  strength  in  purely  riveted 
work  is  due  to  the  general  nature  of  such  designs.  In 
the  first  place,  as  built  in  this  country,  the  bars  or  pieces 
uniting  at  the  panel-points  do  not  assemble  in  the  axial 
lines  of  the  truss,  thus  producing  a  complexity  of  cross 
strains  unknowable  in  amount.  In  a  large  bridge,  in- 
volving heavy  pieces  and  large  joints,  it  is  impossible  to 
so  dispose  the  rivets  as  to  distribute  the  strain  equally 


RIVETED    WORK.  45 

p 

among  them,  although  they  can  only  be  proportioned 
on  that  supposition.  It  will  be  apparent  to  any  one,  on 
a  moment's  reflection,  that  when  two  pieces  of  iron  are 
riveted  together  through  the  medium  of  a  splice-plate, 
the  rivets  at  the  ends  of  the  splice  are  the  first  ones  to 
feel  the  effect  of  a  strain  in  the  bars,  and  consequently 
are  brought  into  action  before  the  rivets  at  the  middle 
of  the  splice  are  affected  ;  and  if  the  bars  are  large,  the 
splice-plate  long,  and  the  rivets  numerous,  it  is  doubtful 
if  the  rivets  in  the  middle  of  a  splice  do  any  service 
whatever ;  certainly  not  before  the  iron  has  stretched 
considerably,  in  which  case  the  first  rivets  may  have  upon 
them  double  the  strain  they  were  calculated  to  bear. 
As  manufactured  in  this  country,  the  holes  of  each  piece 
,are  separately  punched  from  wooden  templates,  and  de- 
spite all  the  care  exercised,  the  drift-pin  must  be  always 
at  hand  to  force  the  matching  of  the  holes  of  contiguous 
plates,  to  admit  the  insertion  of  the  rivet,  thus  developing 
initial  strains  on  the  iron  impossible  to  compute,  which 
may  be  regarded  as  another  very  serious  indictment  of 
riveted  work.  Workmen  can  not  always  be  watched,  and 
the  eyes  of  even  the  fiercest  inspector  can  not  keep  every 
hole  and  rivet  before  him.  The  carelessness  of  a  work- 
man may  be  rapidly  and  nicely  covered  up  with  a  neatly- 
shaped  rivet-head,  which  tells  no  tale  of  the  horribly  muti- 
lated holes  beneath,  to  which  a  cold-chisel  had  possibly 
been  applied,  or  perchance  the  holes  overlapped  too  badly 
for  the  drift-pin  to  even  give  an  appearance  of  matching. 
Another  imperfection  very  apt  to  creep  in  when  hand- 


46  IRON    HIGHWAY    BRIDGES. 

nveting  is  employed,  and  one,  too,  that  is  so  thoroughly 
concealed  as  to  be  impossible  of  detection,  is  the  imperfect 
filling  of  the  holes.  The  chances  of  such  a  serious  defect 
increase  with  the  number  of  the  plates  riveted  together, 
and  owing  to  the  shrinkage  of  the  hot  driven  rivet- 
heads,  they  bind  so  closely  to  the  surfaces  of  the  outer 
plates,  that  striking  with  a  hammer  to  test  "  looseness  "  is 
a  very  fallacious  test.  The  high  strain  under  which  rivet- 
heads  are  left  through  shrinkage  in  cooling  is  often  shown 
by  their  apparent  brittleness  when  cut  off  by  a  cold-chisel. 
They  will  at  times  snap  off  like  a  piece  of  glass  under 
the  first  blow.  A  hand-driven  rivet  will  very  frequently 
drop  out  from  its  own  weight,  when  once  the  head  is 
knocked  off,  showing  that  the  shank  of  the  rivet  shrinks 
away  from  the  holes,  and  when  this  is  not  the  case,  they 
are  as  apt  to  retain  their  position  through  the  distortion 
caused  by  unmatched  plates  as  to  a  perfect  filling  of 
the  holes.  In  Europe,  where  the  riveted  system  has 
been  developed  to  its  utmost  perfection,  these  inherent 
defects  are  recognized,  as  is  shown  by  the  great  care  with 
which  their  riveted  work  is  manufactured,  such  as  drill- 
ing the  rivet-holes  through  the  plates  and  pieces  to  be 
joined  while  clamped  in  position,  and  thus  overcoming 
almost  entirely  the  evil  effects  of  drifting  and  distorted 
rivets.  Power-riveting  is  largely  employed,  as  by  that  mode 
alone  there  is  any  reasonable  certainty  of  filled  holes. 
Did  American  girder-shops  pursue  the  European  system, 
our  riveted  bridges  would  cost  much  more  than  they 
now  do,  and  they  would  be  proportionately  better.  To 


THE    AMERICAN    SYSTEM.  47 

• 

do  this,  however,  requires  more  than  the  customary 
standard  plant — namely,  a  punch,  a  pair  of  shears,  and 
drift-pins,  which  any  old  boiler-shop  can  furnish.  Before 
leaving  the  subject  of  riveted  work,  it  is  well  to  call 
attention  to  "  field-riveting  "-—that  is,  where  spans  are  so 
large  that  they  must  be  shipped  in  parts,  which  are 
riveted  together  in  the  final  position  of  the  work. 
Whatever  objection  has  been  urged  against  skop-nvet- 
ing  is  intensified  in  a  high  degree  when  the  field-riveter 
steps  in  to  do  his  part  of  the  work.  He  must  work  in 
constrained  positions  and  in  all  sorts  of  weather.  If  the 
work  in  the  shop  has  been  well  done,  that  in  the  field  is 
pretty  sure  to  be  badly  done ;  and  as  this  last  applies 
principally  to  the  joints,  the  most  vital  parts  of  the 
whole  structure,  the  work  must  be  judged  entirely  by 
them.  In  contrast  with  riveted  work,  we  have  the  ma- 
ckine-m&die  bearings  and  connections,  which  may  be 
attained  either  by  means  offlms  or  screw-ends,  or  a  com- 
bination of  both.  It  is  through  the  adoption  of  this 
constructive  idea  that  the  Americans  have  been  able  to 
surpass  the  rest  of  the  world  in  bridge-building. 

This  American  system,  as  it  is  universally  called,  per- 
mits of  the  most  economical  use  of  material  possible,  is 
wonderfully  well  adapted  for  long  spans,  and  enables 
the  engineer  to  select  the  quality  and  shape  of  material 
best  adapted  for  any  given  portion  of  his  design.  It  is 
a  system  that  permits  of  closer  harmony  between  theory 
and  practice  than  is  possible  to  attain  in  the  European 
method  or  its  American  imitation,  concerning  which 


48  IRON    HIGHWAY    BRIDGES. 

enough  has  been  said  to  show  how  lamentably  deficient 
that  system  is  in  this  particular.  In  a  bridge  on  the 
American  system,  the  strains,  being  axial,  coincide  with 
the  skeleton  diagram  of  the  truss,  and,  further,  the  strains 
can  be  accurately  computed,  and  need  have  no  more  mate- 
rial provided  to  meet  their  action  than  is  absolutely  neces- 
sary. The  more  usual  mode  of  connection  in  this  system 
is  by  means  of  pins,  which  joints,  when  well  designed  and 
executed,  leave  nothing  to  be  desired.  The  main  points 
to  be  considered  are  the  sizes  of  the  pins,  the  reinforc- 
ing of  the  upper  chord  and  post-bearings,  the  fit  between 
the  pins  and  eyes,  the  proportion  of  the  heads  of  the 
tension-bars,  and  the  uniformity  in  lengths  of  similar 
parts  in  each  panel.  It  is  no  part  of  a  book  of  this 
character  to  give  specific  rules  for  the  proper  proportion 
of  these  parts,  but  the  great  importance  of  the  subject, 
and  the  fact  that  the  majority  of  American  highway 
bridges  are  very  deficient  in  "joint  proportion,"  warrant 
an  attempt  to  make  clear  the  requirements  of  the  pin- 
connection.  Pins  can  not  be  made  too  large,  and  are 
governed  in  size  by  the  largest  tension  eye-bars  through 
which  they  pass.  These  occur  in  the  lower  chord  or  in 
the  main  diagonals  at  the  ends  of  a  truss.  Whether  a 
pin  is  a  half  inch  more  or  less  in  diameter  is  an  econo- 
my not  worth  consideration — only  be  sure  that  the 
error,  if  any,  is  toward  the  larger  diameter.  Considering 
the  very  great  importance  of  properly  proportioned 
pins,  it  is  somewhat  remarkable  that  so  little  attention 
has  been  given  to  the  subject.  For  years  the  crude  con- 


PINS    AND    EYES.  49 

elusions  of  Sir  Charles  Fox,  drawn  from  very  meagre 
experiments,  made  more  than  a  dozen  years  since  in 
England,  have  been  a  sort  of  blind  guide  for  engineers. 
They  have  been  supplemented  within  the  last  five  years 
by  the  experiments  of  Mr.  Berkeley,  also  English  ;  and 
although  these  last  and  more  complete  experiments 
have  shown  how  erroneous  Sir  Charles  Fox's  rules  are, 
yet  those  rules  are  still  given  in  modern  text-books  as 
proper  practice.  Mr.  Charles  Bender,  C.E.,  has  very 
ably  investigated  the  subject  theoretically,  and  shows 
the  various  influences  operating  to  modify  the  size  of 
pins,  according  to  the  position  of  the  different  bars  as- 
sembled upon  them,  and  he  shows  the  fallacy  of  deriving 
rules  from  experiments  made  upon  bars  having  a  uniform 
ratio  of  width  to  thickness,  or  on  pins  only  exposed  to  di- 
rect shearing  action.  The  best  experiments  and  theoretical 
investigations  go  to  show  that  the  size  of  pins  for  flat 
bars  should  be  not  less  in  diameter  than  T8¥  the  width  of 
the  bar,  and  for  square  bars  their  diameter  should  be  not 
less  than  if  times  the  side  of  the  square.  It  will  be 
noticed  that  these  proportions  result  in  pins  enormously 
in  excess  of  what  would  be  necessary  for  simple  shear- 
ing. For  example,  a  bar  4x1  requires  a  pin  3^  inches 
in  diameter,  the  area  of  section  of  which  is  8J  square 
inches,  while  that  of  the  bar  is  but  4  inches.  Pins  should 
be  carefully  turned  to  gauge,  and  fit  the  holes  through 
which  they  pass  with  the  least  play  with  which  it  is  pos- 
sible to  put  the  work  together,  which  the  best  practice 
has  established  at  about  -  of  an  inch.  Of  as  much 


5O  IRON    HIGHWAY    BRIDGES. 

importance  as  the  pins,  is  the  proper  form  to  be 
given  to  the  ends  of  the  "links"  or  "eye-bars,"  the 
name  usually  given  to  the  braces  and  lower  chord  bars. 
In  order  that  the  pin  will  not  tear  through  the  eyes  before 
the  body  of  the  bar  is  at  the  point  of  rupture,  experiment 
has  shown  that  the  link-heads  must  be  full,  and  of  gradual 
curvature,  the  proportions  of  which  being  dependent  some- 
what on  the  mode  of  manufacture.  Still  further  experi- 
ments are  required  on  eye-bars  of  various  sizes,  to  deter- 
mine with  accuracy  just  what  proportion  should  be  given 
to  the  heads ;  but  so  far  as  experience  has  gone,  it  points 
to  a  proportion  in  the  case  of  flat  bars  of  about  50  per 
cent  of  metal  through  the  pin  in  excess  of  that  through 
the  body  of  the  bar,  and  in  front  of  the  pin  about  the 
same  as  is  contained  in  the  body  of  the  bar.  Back  of 
the  pin,  the  curve  uniting  the  head  with  the  body  of  the 
bar  should  be  a  gradual  one,  so  that  the  strain  in  the  bar 
will  not  be  too  abruptly  transferred  around  the  pin.  The 
annexed  cut  represents  the  end  of  an  eye-bar,  with  a  pin 
passing  through  it,  the  relative  intensity  of  the  surface 
pressure  being  indicated  in  shaded  lines.  It  will  be  per- 
ceived how  important  it  is  to  have  tight-fitting  pins, 
since  the  first  pressure  is  simply  a  line  of  contact,  the 
semi-circumference  of  the  pin  only  coming  into  bearing 
when  the  pressure  has  upset  the  metal  in  front  of  the  pin 
by  an  amount  equal  to  the  extent  of  play  in  the  eye. 
Some  engineers  consider  that  the  bearing  surface  should 
be  determined  by  projecting  the  semi-circumference  on 
the  diameter,  allowing  nothing  for  frictional  resistance 


EYE-BARS. 


when  the  pin  and  eye  surfaces  are  in  full  contact.     In 
that  view  of  the  case  for  flat  bars,  with  heads  uniform 

in  thickness  with  the 
body,  pins  should 
have  a  diameter  equal 
to  the  full  depth  of 
the  bar;  or,  in  case 
it  is  unadvisable  to 
have  such  large  pins, 
the  required  bearing 
area  can  be  made  up 

, 


FIG.    14.    LINK    OR    EYE-BAR    HEAD,    SHOWING 
RELATIVE   INTENSITIES   OF    PRESSURE   ON   PIN. 


eyes. 


When  square  bars  are  used,  the  eyes  should  be  formed 
by  long  loop-welds,  which  gives,  of  course,  ample  mate- 
rial around  the  pin,  being  equal  to  the  side  of  the  square. 
Round  bars  should  be  forged  with  an  equivalent  flat  head, 
as  it  is  impossible  to  properly  loop-weld  a  "  round,"  and 
have  a  satisfactory  flat  bearing  on  the  pin.  The  eyes  of 
all  links  should  be  carefully  bored  to  match  the  pin,  with 
minimum  clearance  compatible  with  erection  of  the  work. 
Since  in  all  link  bridges  each  individual  bar  is  calculated 
to  perform  a  given  proportion  of  duty,  uniformity  of 
length,  particularly  in  bars  of  the  same  panel,  is  of  the 
first  importance.  Otherwise,  an  inequality  of  strain  will 
result  after  the  work  is  erected,  the  tighter  bars  taking  all 
the  load  at  first,  only  bringing  the  slack  ones  into  play 
after  they  have  stretched  a  sufficient  amount  so  to  do. 
These  errors  of  length  creep  in  from  two  causes  — 


52  IRON    HIGHWAY    BRIDGES. 

namely,  carelessness  in  centring  the  eyes  from  the 
master-gauge,  and. the  variations  of  temperature  at  which 
they  are  bored.  The  best  shops  use  double-end  boring- 
machines  mounted  on  wrought-iron  beds,  and  if  care  is 
taken  that  the  bars  have  been  long  enough  lying  in  the 
same  temperature  as  that  of  the  machine,  the  second  class 
of  errors  are  removed  to  a  remote  possibility ;  the  avoid- 
ance of  the  first  being  simply  a  matter  of  shop  system, 
in  checking  measurements  and  using  intelligent  supervi- 
sion. 

Flat  eye-bars  (the  form  now  almost  universally  used 
by  the  best  designers)  are  manufactured  in  America, 
either  by  welding  the  eyes  previously  forged  into  shape 
to  the  ends  of  the  bars,  by  die-forging  under  a  steam- 
hammer,  or  upsetting  by  means  of  steam  or  hydraulic 
power.  The  former  process  is  purely  a  welding  process, 
and  should  be  performed  with  great  care  in  a  hollow  coke 
fire,  the  form  of  weld  known  as  the  split  weld  being 
used.  The  second  process  is  a  weld  to  the  extent  that  a 
slab  is  forged  down  on  the  ends  of  the  bar  under  the 
powerful  blows  of  a  steam-hammer,  the  shaping  being 
performed  at  the  same  instant,  the  anvil  and  the  hammer 
having  matched  die-faces,  while  the  latter  process  con- 
sists in  forcing  the  ends  of  the  bar  itself  into  properly- 
shaped  moulds  or  dies  under  an  intermittent  or  a  steady, 
continuous  pressure  of  a  ram,  the  ends  being  previously 
heated  to  a  white  heat.  All  these  processes  are  in  use, 
and  have  given  satisfaction ;  but  the  two  latter  have 
decidedly  the  preference  among  engineers,  owing  to 


MANUFACTURE    OF    EYE-BARS.  5J 

f 

their  greater  reliability.  The  second  method  is  the 
most  flexible,  in  that  there  are  no  such  limitations  of 
ratio  of  width  to  thickness  as  the  direct  upsetting  pro- 
cess necessitates.  One  fact  in  regard  to  upset-bars  must 
not  be  overlooked,  and  that  is  the  distortion  of  the 
fibre,  and  consequent  change  in  the  character  of  the  iron. 
This  is  sure  to  be  extreme,  if  the  operation  is  performed 
under  too  low  pressure,  or  if  the  bar  is  heavy  and  the 
head  large,  in  proportion  to  what  may  be  called  the 
mass  of  the  upsetting-machine.  Where  bars  are  wide 
and  thin,  there  is  a  very  great  distortion  of  fibre  since 
a  large  amount  of  iron  must  be  forced  back  to  fill 
the  moulds,  and  which  a  slight  etching  with  acid 
will  develop  very  clearly.  It  is  owing  to  the  dete- 
rioration of  the  iron  in  the  heads  of  upset-bars  that 
American  experiments  have  resulted  in  somewhat  dif- 
ferent proportions  from  those  made  in  England  on  bars 
of  English  manufacture.  Whether  upsetting  is  done  by 
repeated  impact,  or  by  the  steady,  continuous  pressure  of 
the  hydraulic  ram  fed  from  an  accumulator,  there  is  a 
marked  difference  in  the  result.  Iron  is  most  susceptible 
to  change  of  form  without  deterioration  when  operated 
upon  in  a  highly  heated  state,  and  since  a  bar  commences 
to  cool  the  moment  it  is  taken  out  of  the  furnace,  the  most 
rapid  means  of  shaping  it  will  injure  it  the  least.  A 
fibrous  bar,  operated  upon  in  a  cold  state,  will  be  so  modi- 
fied in  its  molecular  arrangement  as  to  become  crystal- 
line. Again,  in  operating  upon  the  end  of  a  bar,  just  from 
the  heating  furnace,  it  must  of  course  be  firmly  gripped 


54  IRON    HIGHWAY    BRIDGES. 

behind  the  die,  and  where  the  iron  is  comparatively  cold. 
In  the  case  of  slow,  upsetting  by  impact,  the  iron  is  grad- 
ually crowded  back  from  the  soft  end,  the  effect  of  each 
blow  being  less  and  less  as  the  metal  gets  cooler  and  the 
fibres  become  compacted.  At  the  end  of  the  operation, 
the  metal  will  have  chilled  off  rapidly,  and  near  the  base 
of  the  upset  be  almost  cold.  At  the  point  of  "  grip  "  the 
metal  becomes  more  or  less  crystallized,  according  to  the 
temperature  at  that  point.  In  view  of  this  effect  of  tem- 
perature on  iron,  it  follows  that  upsetting  should  be  only 
performed  by  continuous  pressure,  by  means  of  which  the 
iron  may  be  driven  back  in  the  die  at  welding  heat,  at  one 
stroke  of  the  piston. 

Screw-ends  are  sometimes  used  for  the  upper  ends  of 
the  diagonals,  and  form  their  connection  with  the  top 
chord  through  the  medium  of  a  casting,  which  requires  a 
very  awkward  and  ugly  enlargement  to  admit  of  their 
passage.  Screw-ends  should  be  enlarged  over  the  body 
of  the  bar  by  upsetting,  so  that  the  cutting  of  the  screw- 
threads  will  not  diminish  the  sectional  area.  A  serious 
objection  to  the  use  of  screw- ends  arises  from  the  fact 
that  they  are  a  temptation  to  those  custodians  of  public 
works  who  have  a  mania  for  screwing  up  any  thing  they 
can  get  a  wrench  around,  and  so,  in  their  efforts  to  "  ad- 
just "  a  bridge,  they  are  very  apt  to  leave  the  diagonals 
under  different  degrees  of  tension.  To  adjust  screw-ends 
properly,  the  workman  must  combine  the  "  feel "  of  the 
wrench  with  the  striking  of  the  bars,  so  as  to  judge  of  the 
tension  by  the  sound,  which  involves  somewhat  of  a  mu- 


POSTS    AND    THEIR    STRENGTH.  55 


. 


sical  ear,  not  possessed  by  every  mechanic.  Practically  it 
is  impossible  to  tap  nuts  so  that  they  correspond  with  the 
threads  of  the  screw.  The  dies  will  wear,  no  matter  how 
carefully  they  may  have  been  hardened,  and  the  harden- 
ing process  itself  must  affect  the  character  of  the  threads. 
The  post  connection  with  a  pin  is  made  through  the 
medium  of  "  shoes  "  or  "  bases,"  either  of  wrought  iron  or 
cast,  or  both  combined,  depending  on  the  form  of  post 
used.  The  bearing  on  the  pin,  or,  in  other  words,  the 
thickness  in  inches  of  that  portion  of  the  shoe  through 
which  the  pin  passes,  should  be  not  less  than  the  com- 
pressive  strain  (as  exhibited  in  the  line  diagram  of  strains 
which  ought  to  accompany  all  proposals)  in  pounds,  di- 
vided by  twelve  thousand  times  the  diameter  of  the  pin. 
The  sections  of  posts  in  ordinary  use  are  exhibited  here- 
with in  the  order  of  their  relative  theoretical  merit.  The 


FIG.    15.    SECTIONS   OF   POSTS   OR    STRUTS. 

first  is  the  Phoenix  hollow  column  ;  the  next  four  are 
made  from  solid  rolled  sections,  and  the  last  and  weakest 
are  compounded  sections,  as  shown.*  The  resisting  power 
of  posts  is  based  upon  the  ratio  of  their  length  divided 
by  their  diameter,  and  also  upon  the  fact  of  their  having 
round  or  square  end  connections.  For  the  first  five  sec- 

*  The  last  four  sections  are  the  forms  of  struts  used  in  riveted  work,  and 
it  needs  not  the  eye  of  an  expert  to  realize  that  they  are  immeasurably  inferior 
,to  any  of  the  preceding  sections. 


5  IRON    HIGHWAY    BRIDGES. 

tions,  the  diameter  to  be  taken,  in  determining  above  ratio, 
is  the  least  side  of  the  least  rectangle  with  which  they 
can  be  circumscribed.  For  the  other  sections,  two 
thirds  of  the  least  side  must  be  taken  for  the  diameter. 
While  this  method  of  determining  effective  diameters  is 
not  absolutely  accurate,  it  is  sufficiently  near  the  truth  to 
test  the  merit  of  competitive  designs.  Where  a  post  bears 
directly  on  a  pin,  it  should  be  regarded  as  having  a  round 
end.  There  is  probably  no  property  of  iron  about  which 
less  is  positively  known  than  its  real  strength  when  in  the 
form  of  posts  or  columns.  Certain  general  laws  have 
been  determined  by  the  experiments  thus  far  made, 
among  the  most  important  of  which  are  the  following  : 

The  strength  of  a  column  with  square  end  bearings 
being  called  unity,  that  of  a  column  with  both  ends 
rounded  (like  the  ends  of  an  egg)  will  be  one  third,  and 
that  of  a  column  with  one  end  square  and  one  end 
round  will  be  a  mean  between  the  first  two.  That  is, 
the  numbers  i,  f  and  \  represent  the  relative  strength 
of  columns,  according  as  the  bearings  are  square,  one 
round  and  one  square,  or  both  round.  The  formula 
mostly  in  use  for  computing  the  strength  of  posts  is  an 
empirical  one,  invented  by  Lewis  Gordon,  of  England, 
and  is  based  upon  the  experiments  made  for  the  British 
Board  of  Trade,  by  Eaton  Hodgkinson,  about  1840. 
Gordon's  formula  is  simpler  in  application  than  those  de- 
duced by  Hodgkinson,  and,  when  properly  applied,  expe- 
rience has  shown  it  to  be  abundantly  safe.  The  original 
formula  is  as  follows  for  square-end  columns,  and  should 


STRENGTH    OF    COLUMNS.  57 

9 

be  corrected  for  pin  or  round  bearings  by  one  of  the 
three  laws  above  given : 

T-V       T  .        i      j    r       )  36,000  x  area  section 

Breaking:  load  for  (  —  7T^  — 2 

s,      .  >•  =  i      /length  of  column\ 

wrought-iron        i       i  +  -  ~j--— 

}  3000  \         diameter        / 

The  same  formula  for  cast-iron,  using  80,000  in  nu- 
merator of  fraction  instead  of  36,000,  and  -%fa  in  denomi- 
nator instead  of  ^oVo"-  The  constants  in  the  numerator 
are  intended  to  represent  the  average  crushing  strength  of 
a  short  piece  of  the  respective  kinds  of  iron.  Modern 
experiments  have,  however,  shown  that  the  ultimate 
crushing  strength  of  American  wrought-iron  is  much 
higher  than  that  assumed  in  the  formula — namely,  36,000 
Ibs.  per  square  inch,  by  at  least  20  or  25  per  cent,  In 
fact,  so  much  depends  upon  the  kind  of  iron,  that  no  one 
constant  is  suitable  for  undeviating  use.  A  column  made 
from  a  hard  iron  inclined  to  granular,  as  it  should  be, 
will  resist  crushing  better  than  a  soft  fibrous  iron,  or  one 
of  great  tenacity,  and  consequently  a  much  higher  con- 
stant may  be  used.  The  following  table  has  been  com- 
puted from  Gordon's  formula,  using  45,000  in  numerator 
instead  of  36,000,  for  wrought-iron — that  for  cast-iron  re- 
maining the  same  as  in  the  original  formula.  It  must 
be  understood  that  any  of  the  published  tables  for  the 
strength  of  columns  are  purely  tentative,  to  be  modified 
by  such  light  as  farther  experiments  alone  can  give,  and 
which  it  is  hoped  that  the  present  Government  Com- 
mission on  the  "  Strength  of  Iron  and  Steel,"  appointed 
by  Congress  in  the  spring  of  1875,  will  early  institute. 


IRON    HIGHWAY    BRIDGES. 


TABLE  SHOWING  THE  BREAKING  STRENGTH  PER  SQUARE 
INCH  OF  WROUGHT  AND  CAST  IRON  COLUMNS,  COMPUT- 
ED FROM  GORDON'S  FORMULA  : 

Crushing  strength  of  wrought-iron  taken  at  45,000  Ibs.  per  square  inch. 

•'  cast  "        "      "  80,000    "      " 

Values  given  are  in  pounds  for  each  square  inch  area. 


Ratio  of  Length 
to  Diameter. 
See  page  56. 

i. 

Breaking  Load  : 
Square  Ends. 

II. 
Breaking  Load  : 
Round  Ends. 

in. 

Breaking  Load  : 
One  Round,  One 
Square. 

i    Wrought 
Iron. 

Cast 
Iron. 

Wrought 
Iron. 

Cast 
Iron. 

Wrought 
Iron. 

Cast 
Iron. 

10 

15 

20 

25 
30 

35 

40 

45 
5o 

43562 
41860 
39717 
37251 
34615 
31960 

29355 
26866 

24545 

64000 
5I2OO 
4OOOO 
31220 
24617 
19692 
I6OOO 
13196 
II035 

I452I 
13953 
13239 
I24I7 

HS3« 

10653 

97*5 
8955 
8182 

21333 

17067 

13333 
10407 
8206 
6564 

5334 
439^ 
3678 

20042 
27906 
26478 
24834 
23076 
21306 
19570 
I79IO 
16364 

42666 

34134 
26666 
20814 
16412 
I3I28 
10668 
8798 
7356 

FIG.  16.     TOP     CHORD     SECTIONS 


FOR   PIN   CONNECTIONS. 


RIVETED   SYSTEM 


The  tipper  chord  has  often  a  similar  section  to  that 
of  the  posts,  but  when  not  circular  is  usually  shaped  like 
a  box,  the  sides  of  which  are  channel  or  beam  irons, 
and  the  top  a  broad  plate.  The  under  side  of  such  a 
box,  when  open,  should  be  stiffened  with  diagonal  lattic- 
ing or  broad  batten-strips,  so  as  to  aid  in  the  preservation 


TOP    CHORD    SECTIONS.  59 

0 

of  its  form  under  the  compressive  strain  to  which  it  is 
subjected.  The  allowable  strain  per  square  inch  on 
chords  is  governed  by  the  same  rule  as  that  for  columns ; 
the  ends  being  considered  square,  and  the  length  of  the 
chord  the  distance  between  two  panel-points.  The  top 
chord  may  have  simple  machine-faced  butt  joints,  or  it 
may  be  made  continuous  in  sections,  the  contiguous  abut- 
ing  surfaces  being  joined  by  fish  or  splice  plates  riv- 
eted or  bolted  to  them.  Such  plates  serve  simply  to  keep 
the  chord  in  position,  and  are  not  subjected  to  any  strain 
whatever.  Under  this  last  arrangement,  there  would  be 
attained  all  the  advantages  that  can  possibly  be  claimed 
for  riveted  work — namely,  perfect  continuity  of  material. 
This  principle,  combined  with  the  American  system,  re- 
sults in  a  structure  that  harmonizes  theory  and  practice 
in  the  highest  attainable  degree.  With  some  forms  of 
compressive  sections,  like  the  Phoenix  column,  or  the 
three-beam  section,  it  is  desirable,  in  fact  necessary,  that 
a  casting  be  introduced  to  connect  the  several  parts  that 
cluster  at  the  panel-points.  This  casting  must  have  all 
its  bearings  machine-faced  to  match  the  faced  ends  of  the 
chords  and  posts.  In  continuous  box-shaped  chords,  the 
pin-holes  must  be  reinforced  with  thickening  plates,  not 
only  to  increase  pin-bearing,  but  also  to  distribute  the 
pressure  delivered  to  the  chord  at  each  panel-point  over 
as  much  surface  as  possible.  Further,  it  is  advisable  that 
the  increased  sectional  area  required  at  each  panel-point, 
in  approaching  the  centre,  be  placed  in  the  sides  of  the 
box,  as  it  is  through  the  sides  that  the  pin  passes.  It  is 


6O  IRON    HIGHWAY    BRIDGES. 

not  one  of  the  least  of  the  excellencies  of  the  pin-con- 
nection system  that  the  chords,  posts,  and  tension-mem- 
bers may  be  made  to  unite  at  the  centre  of  their  several 
sections,  and  by  proportioning  the  box  chord  as  above 
this  may  be  accomplished  very  fully.  The  advantage  of 
a  cast-iron  joint  box  consists  in  the  very  perfect  attain- 
ment of  this  principle,  as  such  boxes  insure  an  absolutely 
uniform  distribution  of  pressure  over  the  surfaces  of  con- 
tiguous chord  sections.  This  principle  is  about  as  far  lost 
sight  of  in  riveted  work  as  it  is  possible  to  be.  In  such 
work  the  chords  have  no  stiffening  along  the  inner  edges 
of  the  vertical  plates  or  sides  to  which  the  web  system  is 
riveted,  and  the  increase  of  area  is  made  by  riveting  on 
plates  to  the  upper  side  of  the  top  chord,  or  lower  side 
of  the  bottom.  The  centre  of  section  is  not  at  the 
middle  of  the  sides,  as  usually  assumed,  but  approaches 
the  top  or  bottom  plates,  and  in  large  spans,  where  the 
strains  are  great,  necessitating  a  large  area  of  section 
(placed  mostly  in  the  above  plates),  the  centre  of  section 
approaches  the  plates  very  rapidly.  In  applying  the  for- 
mula for  posts,  therefore,  to  such  chord  sections,  the  dia- 
meter used  for  determining  the  ratio  of  "  length  to  diameter" 
must  not  be  taken  as  equal  to  the  side  of  the  least  circum- 
scribing rectangle,  but  must  be  a  much  smaller  quantity. 
Just  what  this  quantity  is  may  be  ascertained  by  reference 
to  special  treatises  on  engineering,  since  it  involves  con- 
siderations too  technical  to  introduce  into  a  book  of  this 
character.  It  will  be  sufficient  for  our  purpose  if  the 
reader  realizes  that  a  box  or  trough-shaped  compression 


AMERICAN    AND    RIVETED    SYSTEMS    COMPARED.        6 1 

d 

chord,  having  most  of  its  metal  on  the  upper  side,  is 
weaker  than  one  which  has  the  metal  equally  distributed 
among  the  three  sides,  and  for  the  weaker  chord  proper 
allowance  must  be  made. 

In  "pin-connection"  chords,  the  pin-holes  must  be 
bored  with  the  same  care  as  eye-bars;  the  maximum 
play  between  pins  and  holes  not  being  permitted  to  much 
exceed  -^  of  an  inch. 

From  what  has  been  said,  in  describing  the  various 
systems  of  bridge-building  in  use — namely,  the  "  riveted," 
the  "  pin,"  and  "  screw-end"  connections — it  will  be  under- 
stood how  it  is  that  the  two  latter  can  be  worked  very  close 
to  absolute  theory,  thus  enabling  material  to  be  disposed  in 
the  best  possible  way  to  concentrate  strains  at  centres  of 
sections,  and  distribute  them  in  axial  lines  through  the 
various  parts  of  the  structure.  Further  than  this,  the 
shape  of  material  used  in  designing  on  these  systems  is 
such  that  proper  grades  of  iron  are  readily  attainable. 
The  riveted  system  has,  of  necessity,  so  many  imper- 
fections of  design,  of  workmanship  and  material,  in 
contrast  with  the  above,  that,  to  obtain  any  thing  ap- 
proaching equal  strength  on  the  same  specification,  it 
should  only  be  used  with  a  higher  factor  of  safety. 
It  is  probable  that  this  difference  is  not  less  than  20  per 
cent ;  so  that  when  a  pin  bridge  is  called  for,  having  a 
factor  of  Jive,  a  riveted  bridge  can  not  be  considered  as 
approaching  the  same  strength  unless  it  is  proportioned 
with  a  factor  of  six.  The  fact  that  a  riveted  bridge  is 
stiff,  or  that  its  deflections  may  be  small  under  a  test,  is  no 


62  IRON    HIGHWAY    BRIDGES. 

evidence    of  strength,   which   last    depends  upon   other 
considerations  than  those  applying  to  stiffness. 

The  stiffness  of  a  girder  depends  upon  the  average 
sectional  area  of  the  flanges  and  web,  while  the  strength 
is  measured  solely  by  the  net  sectional  area  at  any  point. 
A  girder,  for  example,  having  uniform  flange  areas  from 
end  to  end,  would  be  stiffer  than  one  having  this  area 
only  at  the  centre,  and  diminishing  with  the  diminution 
of  strains  toward  either  abutment,  but  it  would  not  be 
stronger.  The  amount  of  metal  at  the  weakest  point 
determines  the  strength  of  the  girder,  and  since  this  is  a 
matter  independent  of  stiffness,  it  follows  that  the  ad- 
vocates of  riveted  work  practice  a  deception  on  the 
public  (perchance  themselves)  in  pointing  to  the  wonder- 
ful stiffness  of  the  lattice  bridge,  as  a  triumphajit  refuta- 
tion of  the  damaging  criticisms  made  by  those  who  have 
well  weighed  the  respective  merits  of  the  various  methods 
of  bridge-building. 

THE  FLOORING  SYSTEM. — If  there  is  one  part  of  a 
bridge  more  than  another  that  can  be  claimed  to  be  of 
supreme  importance,  it  is  the  flooring  system,  to  a  careful 
proportioning  of  which  more  attention  has  been  paid 
during  the  last  few  years  than  ever  before.  A  good,  stiff 
floor  is  a  pretty  fair  criterion  of  the  rest  of  the  work,  as 
well  as  a  comfort  to  the  travelling  public.  The  various 
elements  of  the  floor  system  are  the  cross-beams,  the 
stringers,  the  connection  with  the  trusses,  the  sway-brac- 
ing, and  the  floor-covering. 

The  cross-beams,  often  called  floor  or  needle  beams, 


FLOORING    SYSTEM.  6£ 

(f 

may  be  either  solid  rolled  flange-beams,  single  or  in  pairs, 
or  beams  of  lighter  section  deeply  trussed  ;  or,  finally,  riv- 
eted plate  web-girders,  the  two  last  being  better  than  the 
first — not  that  they  are  necessarily  stronger,  but  from  the 
great  depth  thereby  attainable,  there  is  less  spring  to 

FIG.    17. 


12.  0. 


8.  0- 


HALF    SECTION    PLAINFIELD    BRIDGE. 


SIDE   VIEW   PLAINFIELD    BRIDGE,    104    FEET    SPAN.      BY   THE   AUTHOR. 


64  IRON    HIGHWAY    BRIDGES. 

them  under  rapidly  moving  loads,  with  a  proportionate 
gain  in  stiffness.  In  the  best  designs,  cross-beams  are 
located  at  panel-points,  and  they  must  be  proportioned 
to  carry  the  wheel-loads  previously  indicated.  When 
sidewalks  are  to  be  carried  outside  of  the  trusses,  the  floor- 
beams  of  the  roadway  are  prolonged  on  either  side  to  sup- 
port them,  although  occasionally  circumstances  may  arise 
when  the  sidewalks  must  be  supported  by  independent 
cantilevers  bolted  or  riveted  to  the  outside  faces  of  the 
truss-posts.  All  things  being  considered,  the  compound 
riveted  girder  is  probably  the  best  form  for  floor-beams, 
because  they  can  be  made  deep.  A  good  depth  for  such 
girders  in  the  middle  is  one  tenth  the  width  of  roadway, 
but  for  long  panels  and  heavy  loads  a  still  greater  depth 
will  often  be  found  more  desirable.  A  short  distance 
either  side  of  the  centre,  the  bottom-flange  may  be  tapered 
up  gradually  to  the  point  of  support.  This  form,  even 
when  not  dictated  by  motives  of  economy,  is  very  much 
more  sightly  than  if  the  flanges  are  kept  horizontal  and 
parallel  from  end  to  end/  The  thickness  of  the  web  in 
such  girders  is  usually  from  J  to  T5T  of  an  inch,  and  the 
flanges  should  be  so  arranged  as  to  be  formed  from 
but  two  angle-irons,  the  section  of  which  must,  of  course, 
be  determined  by  the  extreme  strain  at  centre  of  beam, 
This  is  a  matter  easily  attained,  since  the  sizes  of  angles 
vary  so  much  that  any  desired  area  may  be  found  in  the 
lists  of  the  principal  manufacturers.  The  objections 
previously  advanced  against  riveted  work  have  least  force 
in  such  girders  as  are  above  described,  there  being  but  a 


FLOOR-BEAMS    AND    THEIR    RIVETING.  65 

0 

single  line  of  rivets  which  unite  the  solid  flanges  to  the 
web,  and  the  number  and  proportion  of  the  rivets  can  be 
computed  with  a  fair  amount  of  accuracy.  Special  atten- 
tion is  called  to  the  idea  of  solid  flanges,  implied  in  the 
recommendation  for  using  but  two  angle-irons,  as  opposed 
to  a  very  common  practice  of  using  light  angles,  and  in- 
creasing the  sectional  area  toward  the  centre  of  the  beam 
by  riveting  on  plates  to  the  angles,  whereby  the  complex- 
ity of  riveted  work  is  introduced,  which  it  is  desirable 
to  avoid  in  every  instance  where  possible.  Sufficient 
attention  is  rarely  paid  to  the  riveting,  the  pitch  of  the 
rivets  (that  is,  the  distance  from  centre  to  centre)  being 
usually  too  great.  Thin  webs  require  close  riveting,  and 
the  rivets  should  be  well  driven,  by  power  if  possible, 
since  in  this  way  alone  can  any  reliability  be  placed  upon 
the  holes  being  well  filled. 

No  exact  rule  can  be  given  for  the  pitch  of  rivets,  as 
it  is  a  matter  of  computation  in  pounds,  of  just  how  much 
horizontal  strain  is  delivered  by  the  web  at  any  given 
point  to  the  flanges.  As  this  web-strain  increases  to- 
ward the  ends  of  a  girder,  the  rivets  should  be  placed 
closer  as  the  ends  are  approached.  The  pitch  will  vary 
from  3  to  6  inches,  depending  upon  the  above  considera- 
tions, and  the  smallest  size  rivet  that  should  be  used  in 
the  flanges  is  f  of  an  inch,  which  becomes  ^  greater  after 
being  driven,  where  the  hole  is  properly  filled.  The  web 
requires  occasional  stiffeners,  usually  two,  intermediate 
between  supports,  for  ordinary  widths  of  roadway,  and 
one  at  either  point  of  support.  If  the  web  is  of  such 


66  IRON    HIGHWAY    BRIDGES. 

thickness  that  the  distance  between  the  flange  angle-irons 
is  not  greater  than  thirty  to  thirty-five  times  that  thick- 
ness, no  stiffeners  will  be  required.  Since  there  is  no 
difficulty  in  obtaining  the  pieces  composing  a  compound 
girder  in  one  length  between  bearings,  nothing  has  been 
said  about  joints.  Should  these  occur,  either  in  flange 
or  web,  pains  must  be  taken  to  have  splices  of  ample 
size,  and  a  full  complement  of  rivets,  to  thoroughly  trans- 
mit the  strength  of  the  solid  sections  so  united.  Solid 
rolled  beams  are  10  per  cent  stronger  than  riveted  beams, 
but  are  much  more  expensive  per  pound,  the  difference 
at  present  (1875)  being  25  per  cent  and  upward."""  Such 
beams,  in  double-track  roadways,  from  their  shallowness, 
spring  too  much,  throwing  the  trusses  into  an  annoying 
vibration,  to  say  the  least,  even  from  light  passing  loads, 
and  conveying  an  idea  of  weakness,  which  the  structures 
may  not  really  possess. 

The  connection  of  the  floor-beams  to  the  trusses,  for 
deck-bridges,  is  a  very  simple  matter,  as  they  are  then 
directly  bolted  to  the  top  chord.  For  through  bridges, 
or  half-deck  bridges,  they  are  either  hung  from  the  pin 
by  means  of  hanger-bolts,  or  they  are  riveted  or  bolted 
to  the  posts.  When  hung  from  the  pin,  the  hangers  are 
best  of  the  f]  form,  the  legs  being  long  enough  to  pass 
down  the  full  depth  of  the  floor-beam  at  that  point, 
through  a  washer-plate  (by  preference  of  wrought-iron) 

*  Since  the  above  was  written,  the  price  of  beams  has  been  reduced  fully 
the  amount  of  this  difference. 


STRINGER-BEAMS.  67 

•  0 

on  which  the  beam  rests.  The  end  of  each  leg  is  furnish- 
ed with  a  nut,  sometimes  with  a  jam-nut  in  addition; 
which,  when  drawn  up,  holds  the  beam  securely  in  place. 
Inasmuch  as  these  hangers  are  short,  and  always  feel  at 
once  the  effect  of  the  passing  load,  they  should  be  of  first- 
quality  iron,  and  not  be  strained  in  excess  of  8000  Ibs. 
per  square  inch  at  the  root  of  the  screw-thread.  They 
should  have  a  flat  bearing  on  the  pin,  and  may  be  either 
single  or  in  pairs.  When  the  beams  are  riveted  to  the 
posts,  usually  between  them,  the  connection  is  made  by 
means  of  angle-iron  brackets,  one  on  either  side  of  the 
web,  arid  in  length  equal  to  the  whole  depth  of  the  beam 
at  the  bearing,  and  since  this  attachment  depends  solely 
on  the  strength  of  the  riveting,  and  since  the  riveting 
must  be  done  on  the  ground  after  the  work  is  in  posi- 
tion, an  excess  of  rivets  should  be  arranged  for,  to  com- 
pensate for  the  imperfections  of  field-riveting,  which  is 
usually  more  difficult  to  get  at  than  in  the  shop,  and 
consequently  not  so  well  done.* 

The  horizontal  or  sway  bracing  may  consist  of  very 
light  rods,  if  the  floor  is  well  laid,  forming  as  it  does  a 
very  effective  system  of  bracing  against  lateral  movement. 
Rods  from  f  to  i  inch  round  will  cover  all  but  extreme 
requirements,  and  they  are  attached  by  any  convenient 
means  to  the  floor-beams  near  their  point  of  support. 
They  require  a  screw-adjustment  of  some  kind,  turn- 
buckles  or  end-screws,  in  order  that  they  may  be  drawn  up 
taut.  On  top  of  the  floor-beams,  and  lengthwise  with 
the  bridge,  are  laid  the  stringer-beams.  These  beams 

*  See  Plainfield  Bridge,  page  63. 


68  IRON    HIGHWAY    BRIDGES. 

may  be  either  of  wood  or  iron,  and  are  spaced  from  two 
to  three  and  a  half  feet  apart,  depending  on  the  character 
of  the  flooring  and  the  loads  to  which  the  bridge  is  liable 
to  be  exposed.     If  stringers  are  proportioned  for  wheel 
loads,  as  has  been  recommended,  their  size  is  independent 
of  their  distance  apart,  since,  however  great  their  number, 
a  wheel  may  be  immediately  over  any  one,  straining  it  to 
the  maximum.     Where  a  roadway  is  regulated  by  guard- 
timbers,  confining  the  wagon-tracks  to  a  fixed  position, 
the  stringers  may  be  made  heavier  immediately  under  the 
track-way,  and  lighter  under  the  rest  of  the  flooring.  For 
wooden  stringers,  white  or  yellow  pine  is  the  best  kind 
of  timber,  such   varieties  of  timber   being   obtained    of 
straighter  grain  than  most  any  other,  and  consequently 
are    peculiarly   well   adapted   for  resisting  the    effect  of 
transverse  strain.     Stringer  timbers  should  be  inspected 
with  greater  care  than  is  given  to  the  floor-planks,  not 
only  on  account  of  their  position  as  beams,  but  also  be- 
cause floor-planks,  under  most  circumstances,  will  wear  out 
before  they  will  rot  out,  while  the  stringers,  not  being 
exposed  to  the  abrasion  caused  by  horses  and  vehicles, 
become  destroyed  by  decay,  the  date  of  such  destruc- 
tion   being  dependent   on   the  practical  knowledge   of 
the  timber  inspector.     Wooden  stringers  should  be  uni- 
formly notched  down  on  the  cross-beams,  which  not  only 
aid  in  retaining  them  in  their  position,  but  also  insure 
uniformity  in  the  level  of  their  upper  surfaces.     The  fol- 
lowing table  will  be  found  convenient  in   determining 
the  size  of  timber  to  be  used  for  different  panel-lengths : 


PROPER  SIZE  STRINGERS  FOR  GIVEN  WHEEL  LOADS.     69 


Table  giving  proper  size  of  wooden  stringers,  for  supporting  different 
assumed  wheel-loads,  supposed  to  be  concentrated  in  the  middle  of  a 
panel,  the  timber  being  strained  to  1200  Ibs.  per  square  inch. 


LOADS    ON   ONE   WHEEL. 


Span   or  panel-length. 

500  Ibs. 

1000  Ibs. 

1500  Ibs. 

2000  Ibs. 

2500  Ibs. 

10  feet. 

2x8 

3  x     8 

3X9 

3x9 

3  x  10 

12       " 

2x8 

3  x     8 

3  x  10 

3      X    12 

4  x  12 

14     " 

2x9 

3x9 

3  x   ii 

3i  x  12 

3  x  13 

18     " 

2    X    10 

3  x  10 

3  x  12 

3     x   14 

4  x  14 

20       " 

3  x  10 

3  x  12 

4  x   12 

4    x  14 

4  x  16 

Iron  stringers  are  simply  rolled  I  beams,  of  proper 
strength  for  the  wheel  loads,  and  may  be  had  of  any 
depth  from  four  inches  (weighing  ten  pounds  per  foot), 
upward.  Where  they  rest  upon  the  floor-girders,  they 
should  be  secured  by  means  of  bolts,  clips,  or  brackets. 

*  Table  giving  proper  size  of  iron  stringers,  for  supporting  different 
assumed  wheel-loads,  supposed  to  be  concentrated  in  the  middle  of  a 
panel,  the  iron  being  strained  not  over  12,000  Ibs.  per  square  inch. 

LOADS    ON    ONE   WHEEL. 


Span  or 
panel- 
length. 

500  Ibs. 

1000  Ibs. 

1500  Ibs. 

2000  Ibs. 

2500  Ibs. 

10   ft. 
12    " 

15     " 

18   " 

20    " 

4"  61bs.p.ft. 
4"  6  «       '• 
5"  10  " 

6"  1  3  ««       •« 
7"i8  «       " 

4"iolbs.p.ft. 
4"  10  "       " 
5"  10  "       " 
6"  13  " 
7"i8  " 

4"  10  Ibs.  p.  ft. 
4"  10  " 
5"  10  "       " 
6"  13"        •' 

7"i8  "       « 

5"iolbs.  p.ft. 
5"  1  2  " 
6"  1  3  "       " 
7*18  " 
f  1  8  " 

5"  1  2  Ibs.  p.ft. 
6"  13  '*       " 
6"  13"       •• 
7"  18  "       " 
7"i8  "       " 

FLOORING. — The  flooring  of  common  road-bridges  usu- 

*  The  sizes  of  beams  recommended  in  the  table  are  the  nearest  mercantile 
sizes  that  fulfil  the  requirements.  This  in  some  cases  necessitates  the  use  of 
beams  in  excess  of  that  called  for  by  the  loads.  It  was  thought  best  to  use 
none  lighter  than  the  seven-inch  beam  for  the  twenty-feet  panel-lengths,  since 
shallower  beams  would  be  apt  to  spring  to  an  undesirable  extent. 


7O  IRON    HIGHWAY    BRIDGES. 

ally  consists  of  one  course  of  plank,  laid  transversely  to 
the  stringers,  and  about  three  inches  in  thickness.  Occa- 
sionally two  courses  are  used,  in  which  case  it  is  a  good 
plan  to  apply  to  the  lower  course  some  of  the  wood-pre- 
servative processes,  and  the  cost  of  such  application  can 
be  balanced  by  using  a  cheaper  grade  of  timber  than 
would  otherwise  be  proper — such  as  spruce.  If  wooden 
stringers  are  used,  they  may  also  be  chemically  treated, 
when  the  sub-floor  can  be  regarded  as  measurably  per- 
manent, the  only  renewals  being  that  of  the  upper  hard- 
wood plank,  as  it  becomes  worn.  When  two  courses  are 
used,  the  lower  one  should  be  not  less  than  two  and  a  half 
or  three  inches  in  thickness,  and  the  upper  two  inches, 
which  last,  if  laid  diagonally  to  the  lower  course,  will 
materially  stiffen  the  floor  as  a  whole.  The  planking  is 
spiked  directly  to  the  stringers,  if  of  wood,  with  spikes 
having  a  length  of  about  double  the  thickness  of  the 
plank.  When  two  courses  are  used,  each  course  should 
be  spiked  down  independently.  It  is  not  necessary  to 
spike  at  each  stringer  intersection,  every  other  one  being 
sufficient ;  but  where  spiked,  there  should  be  two  spikes 
used,  one  at  either  edge  of  the  plank.  Where  iron 
stringers  are  used,  the  simplest  method  of  securing 
the  floor-plank  is  to  lay  a  spiking  timber  on  either  side 
of  the  roadway,  and  one  or  more  between,  to  which  the 
planks  are  fastened  in  the  usual  way.  This  arrangement 
avoids  the  necessity  of  using  hook  head-bolts,  clinch- 
spikes,  and  other  troublesome  devices  required  if  the  at- 
tachment is  made  directly  to  the  iron.  On  either  side  of 


GUARD-TIMBERS LAYING    SIDEWALKS.  71 


• 


the  roadway  there  should  be  bolted  to  the  flooring,  guard- 
timbers  of  hard  wood,  with  the  inside  edge  chamfered 
off  to  make  a  finish.  These  guards  should  be  located  far 
enough  from  the  trusses  to  prevent  the  wheel-hubs  from 
striking  them,  and  they  should  be  raised  by  means 
of  blocking,  at  intervals  of  five  or  six  feet,  about  three 
inches,  to  aid  the  drainage,  and  add  to  their  effective 
height.  Pieces  of  the  floor-plank,  about  eighteen  inches 
long,  will  be  found  convenient  for  this  blocking.  The 
guard-timbers  had  best  have  lap-joints,  which  laps  should 
be  about  twelve  inches  long,  and  secured  with  two  bolts. 
Where  there  are  sidewalks,  it  is  desirable  to  have  them 
raised  above  the  level  of  the  roadway,  which  can  best  be 
done  by  means  of  hard-wood  bolster-pieces,  at  intervals 
of  about  four  feet,  laid  transversely  with  the  stringers, 
and  of  a  depth  equal  to  the  desired  elevation  of  walk. 
With  sidewalks  projecting  beyond  the  trusses,  necessitat- 
ing a  stiff  independent  railing,  a  rail-base  should  be  fast- 
ened with  two  bolts  to  the  ends  of  the  bolsters,  and  have 
a  projection  of  about  three  inches.  This  rail-base  is  usu- 
ally from  twelve  to  sixteen  inches  in  width,  the  upper 
edges  being  neatly  chamfered,  and  the  exposed  surfaces 
planed.  On  the  inside  edge  of  the  bolsters,  and  bolted 
to  them,  next  the  trusses,  there  should  be  a  deep  guard- 
timber,  at  least  twelve  inches  higher  than  the  walk,  and  if 
desired,  as  an  additional  precaution,  a  few  slats  can  be 
spiked  between  the  sidewalk  and  roadway-guards,  cover- 
ing the  otherwise  open  space  between  them,  unless  it 
happens  that  the  roadway-plank  are  fitted  around  the 


72  IRON    HIGHWAY    BRIDGES. 

posts,  and  carried  close  up  to  the  sidewalk.  With  the 
above  arrangement  for  supporting  the-  sidewalk,  it  is  ne- 
cessary to  lay  the  plank  (about  two  inches  thick)  longi- 
tudinally with  the  bridge,  spiking  to  the  bolsters  with 
two  spikes  at  each  intersection.  It  always  makes  the 
most  satisfactory  walk  to  have  the  planks  narrow,  and 
edged  to  a  uniform  width.  They  should  be  laid  one  half 
inch  apart  to  form  drip-spaces,  and  in  first-class  work  the 
upper  surfaces  of  the  planks  should  have  been  planed 
before  laying,  as  well  as  that  of  the  rail-base  and  inner 
guard. 

The  planed  surfaces  ought  to  be  well  oiled,  not  alone 
as  an  inexpensive  finish,  but  also  to  protect  the  plank  in 
a  measure  from  sun-cracking.  The  best  kind  of  wood,  be- 
yond all  question,  for  sidewalk  plank,  is  yellow  pine. 
The  cornice,  of  i^-inch  clear  pine,  is  fastened  to  the  ends 
of  the  bolster-pieces,  and  a  bold  moulding  is  nailed 
under  the  projection  of  the  rail-base.  A  very  slight  ex- 
pense will  provide  a  neat  scroll "  drop  "  opposite  the  end 
of  each  floor-beam,  which,  trifling  as  it  is,  materially 
adds  to  the  appearance  of  a  bridge.  The  above  descrip- 
tion of  the  floor  may  be  considered  a  standard  method 
for  the  general  type  for  road-bridges  ;  but  in  important 
city  bridges,  floors  should  be  made  very  much  more 
durable  than  has  thus  far  been  customary  in  this  country, 
except  in  a  very  few  localities.  It  is  true  that  durable 
floors,  either  of  wood  or  stone  paving,  add  vastly  to 
the  cost  of  a  structure,  increasing  as  it  does  the  dead 
load  to  be  carried,  but  in  many  cases  it  is  warranted  by 


PERMANENT    FLOORING.  73 

0 

the  circumstances  of  heavy  travel,  the  interruption  to 
which  through  frequent  repairs  (as  would  necessarily  be 
the  case  for  an  ordinary  wooden  floor)  would  cause  great 

FORMS     OF     WROUGHT-IRON     FLOOR-PLATES. 


FIG.  18.  FIG.  19.  FIG.  20. 

BUCKLE-PLATE.  CORRUGATED  PLATE.       ZORE,  OR  FRENCH  SECTION. 

inconvenience.  Any  kind  of  paving  that  may  be  used 
requires  an  iron  floor,  which  may  be  made  of  wrought- 
iron  plates,  -^g-  to  T5^  of  an  inch  in  thickness,  in  the  form 
of  broad  corrugations  laid  transversely,  or  buckle-plates, 
which  are  rectangular  plates  about  3  ft.  square,  domed  or 
crowned  under  pressure  a  height  of  three  or  more  inches 
at  the  centre,  and  having  flat  edges  on  all  four  sides,  to 
allow  of  riveting  to  the  stringer-beams.  The  general 
appearance  of  these  plates  is  that  of  a  flattened  dome. 
After  the  floor  is  thus  formed,  it  must  be  levelled  off 
with  well-made  cement  concrete,  to  a  depth  of  four  inches 
and  upward,  to  form  a  bottom  for  the  paving.  This 
concrete  must  be  prepared  with  great  care,  as  upon  its 
excellence  depends  the  protection  of  the  iron  plates  from 
water,  which,  at  the  best,  it  is  very  difficult  to  keep  from 
working  its  way  through  the  roadway ;  and  as  floor-plates 
are  made  from  comparatively  thin  iron,  perfect  immunity 
from  rust  is  the  price  of  their  durability.  In  view  of 


74  IRON    HIGHWAY    BRIDGES. 

this  fact,  as  an  additional  precaution,  after  the  concrete 
has  been  levelled  off,  or  rather  crowned  to  the  usual  street 
regulations,  and  had  time  to  harden,  it  is  well  to  coat  the 
whole  surface  of  concrete  about  an  inch  thick  with  as- 
phalt mixed  with  fine  ashes,  to  add  to  its  body,  flashing 
it  up  at  least  six  inches  against  all  projections  where  it 
would  be  possible  for  water  to  trace  through  and  get  at 
the  iron  of  the  flooring  system.  On  the  surface  thus  pre- 
pared, the  roadway,  gutters,  and  sidewalks  are  laid  as  in 
the  ordinary  street,  only  with  greater  care.  A  proper 
provision  for  drainage  must  not  be  overlooked,  and  fre- 
quent spouts  ought  to  be  introduced  to  carry  the  water 
rapidly  away,  clear  of  the  trusses.  While  Macadam  and 
stone-block  pavements  have  been  used  for  bridge-plat- 
forms, they  are  enormously  heavy  as  compared  with 
wood,  and,  while  more  expensive  in  themselves  than  a 
wood-block  pavement,  add  very  largely  to  the  genera! 
cost  of  all  the  iron-work,  owing  to  their  excessive  weight. 
Under  most  any  circumstances,  wood  blocks  are  the  best 
for  bridges,  and  if  they  have  a  good,  uniform  bottom  to 
rest  upon,  the  conditions  that  have  caused  the  failure  of 
the  wood-block  pavements  in  most  of  our  cities  are  re- 
moved. Blocks  four  inches  deep  will  answer  all  require- 
ments for  ordinary  traffic,  and  a  depth  of  six  inches  the 
heaviest.  The  blocks  should  not  rest  immediately  upon 
the  prepared  floor  surface,  but  on  tarred,  well-seasoned 
plank,  one  inch  thick,  with  a  thin  layer  of  fine  sand  in- 
terposed between  the  asphalt  and  the  plank. 

BEAM-BRIDGES. — Special    notice   is   directed    to  the 


BEAM-BRIDGES. 


75 


construction  of  beam-bridges,  as  an  economical  substi- 
tute for  the  ordinary  stone  arch  and  culverts  so  much  in 


use  throughout  the  country.  Apart  from  economical 
considerations,  they  afford  an  increased  water-way,  and 
thus  avoid  the  liability  to  disastrous  overflows  during 
sudden  freshets,  as  is  almost  sure  to  be  the  case  when 
a  freshet  meets  with  an  obstruction  like  an  arch,  which, 
if  made  large  enough  to  easily  pass  extreme  floods, 
would  become  comparatively  a  very  expensive  affair. 
There  is  hardly  a  town  or  village  through  which  a  brook 
runs,  that  has  not  suffered  more  or  less  damage  through 
the  incapacity  of  arch  culverts  to  carry  off  the  water  of 
an  unusual  freshet.  Beam-bridges  can  very  readily  be 
carried  up  to  spans  of  25  or  30  feet,  and  if  properly 
designed,  and  the  exposed  parts  occasionally  painted, 
can  be  regarded  as  durable  as  the  old-fashioned  stone 
arch.  The  flooring  of  such  bridges  may  be  simply  plank 
(Fig.  21),  or  it  may  be  made  permanent,  as  before  de- 
scribed, with  iron  floor-plates  and  paving  (as  in  Fig.  22). 


i      i 


FIG.  22.    BEAM-BRIDGE — NICHOLSON  PAVEMENT  ON  BUCKLE  PLATES. 


76  IRON    HIGHWAY    BRIDGES. 

A  very  excellent  floor  is  one  made  with  brick  arches 
turned  between  the  beams,  and  laid  in  cement  mortar, 
very  similar  to  the  ordinary  fireproof  floor  (see  Fig.  23). 


aiiML^illi^  ^^i^^^lij^i^ 


FIG.    23.    BEAM-BRIDGE — TELFORD    PAVEMENT   ON   BRICK   ARCHES. 

The  arches  are  levelled  off  with  concrete,  and  the  pav- 
ing, or  Telford,  laid  on  the  concrete  surface  previously 
coated  with  asphalt.  For  these  bridges,  solid  rolled 
beams  or  compound  plate-girders  are  used,  spaced  from 
3  to  5  feet  apart,  with  tie-rods  at  intervals  connecting 
their  lower  flanges.  The  compound  beams,  not  being 
restricted  in  depth,  and  costing  less  per  pound,  will 
usually  be  found  the  most  desirable.  The  temptation  to 
use  thin  web-plates  in  such  girders,  from  motives  of  econ- 
omy, should  be  avoided,  as  a  percentage  of  rust  must  be 
provided  for,  either  on  account  of  possible  neglect,  or  from 
carelessly-laid  brick-work  and  concrete,  allowing  water 
to  trace  in  alongside  of  the  inaccessible  plates.  Before 
brick  arches  are  turned,  a  further  precaution  than  those 
named  should  be  used,  and  that  is  to  thickly  coat  the 
girders  with  a  tar  paint  of  some  kind.  Perpetuating  the 
life  of  iron-work  is  very  often  simply  a  matter  of  inex- 
pensive, preliminary  precaution,  which,  if  once  realized, 
would  be  oftener  put  in  practice  than  it  is. 


WIDTH    OF    ROADWAYS  AND  SIDEWALKS. 

As  to  the  proper  width  of  roadways  and  sidewalks, 
where  street  regulations  do  not  impose  carrying  the 
whole  width  of  the  street  over  the  bridge,  the  circum- 
stance of  location  is  very  occasional  where  more  than 
two  wagon-ways  are  necessary.  Eighteen  feet  between 
the  side-guard  timbers  are  amply  sufficient  for  all  ordi- 
nary traffic,  and  in  many  cases  sixteen  feet  will  be  found 
sufficient. 

A  greater  width  of  roadway  (excepting  sufficient  width 
is  added  for  a  third  wagon-track)  involves  an  unneces- 
sary expenditure  of  money,  since  the  bridge,  being  pro- 
portioned for  a  certain  number  of  pounds  per  square 
foot,  each  unnecessary  foot  in  width,  requires  just  so  much 
more  material,  which  rapidly  becomes  transformed  into 
dollars,  without  a  particle  of  advantage  accruing.  The 
great  difference  will  be  found  in  the  floor,  since  the  cross- 
beams increase  in  weight  very  rapidly,  as  the  width  of 
the  roadway  increases,  and  the  number  of  stringers  is 
also  increased.  A  rule  then  to  determine  how  wide  a 
roadway  should  be  made  is  to  determine  the  minimum 
width,  with  a  margin  for  clearance,  for  one  wagon-way. 
Then  two  or  three  times,  this,  according  as  there  is  a 
double  or  triple  wagon-way  to  be  accommodated,  will 
give  the  distance  between  roadway-guards.  Sidewalks, 
if  on  either  side,  need  not  be  made  wider  than  four  feet 
in  the  clear;  but  if  only  one  sidewalk  is  to  be  provided, 


78  IRON    HIGHWAY    BRIDGES. 

having  to  accommodate  travel  in  opposite  directions,  a 
width  of  six  feet  in  the  clear  will  be  found  sufficient. 

When  bridges  are  of  such  span  as  to  necessitate  a 
height  of  truss  requiring  overhead  sway-bracing  between 
the  trusses,  a  clear  height  of  from  thirteen  to  fourteen 
feet  above  the  flooring  will  be  found  to  answer  all  but 
extreme  requirements. 

WEIGHTS   OF   MATERIAL,  ETC. 

In  designing  a  bridge,  the  weight  of  the  flooring 
must  be  first  computed,  and  it  is  a  fixed  quantity,  inde- 
pendent of  the  span,  for  the  same  width  of  roadways, 
sidewalks,  and  panel-lengths.  It  forms  the  principal 
part  of  the  dead  load  in  spans  up  to  about  100  feet,  and 
in  addition  to  the  weight  of  material  of  which  it  is  com- 
posed, some  consideration  must  be  paid  in  northern  cli- 
mates to  snow-loads,  which  add  to  the  dead  weight  ten 
to  fifteen  pounds  per  square  foot. 

It  is  impossible  to  give  a  reliable  rule  for  the  dead 
weight  of  the  iron  and  other  materials  entering  into  the 
construction  of  a  bridge,  depending  as  they  do  upon 
peculiarities  of  form  and  construction  ;  but  the  following 
data,  as  far  as  it  goes,  will  assist  any  one  in  determining 
this  important  preliminary  in  proportioning  the  parts  of 
a  given  design.  A  yard  of  wrought-iron,  having  one 
square-inch  section,  weighs  ten  pounds.  So  that,  know- 
ing the  area  in  inches  of  a  given  piece  of  iron,  all  that  is 
necessary  is  to  multiply  it  by  ten  and  divide  by  three,  to 


THE    MAINTENANCE    OF    IRON-WORK.  79 

f 

have  the  weight  per  lineal  foot.  A  cubic  inch  of  cast- 
iron  will  weigh  ten  per  cent  in  excess  of  one  quarter  of 
a  pound.  The  weight  of  timber  varies  according  to  its 
condition,  whether  dry  or  wet,  a  fair  average  being  given 
as  below : 

White  pine,  3  Ibs.  per  sq.  ft.,  B.M.  6  Ibs.  for  2  in.  plank,  9  Ibs.  for  3  in. 
Yellow  "  4  "  "  "  "  8  "  "  "  "  12  "  "  " 

Oak          "    41 "       "     .  "  9   "       "     "        "        131 "       "      " 

FOR   PAVEMENTS. 

Wooden  block,  as  Nicholson,  25  to  35  Ibs.  per  square  foot,  according 
to  depth  of  blocks. 

Telfora  and  Macadam 130  Ibs.  per  cubic  foot. 

Stone  block 150    " 

SUPPORTS   OF   PAVEMENTS. 

Wrought-iron  Buckle-plates,  etc.,  depending  on  thickness :  a  square 
foot  of  one  quarter  inch  plate-iron  weighs  10  Ibs. 

Brick-work,  when  turned  arches  are  used 120  Ibs.  per  cubic  foot. 

Concrete,  for  levelling  off  no  to  130   "       "        "         " 

Gravel.. 120   "       "        "        " 

Hard  asphalt 140   "       "         "         " 

THE   MAINTENANCE   OF   IRON-WORK. 

This  subject  has  not  received  the  degree  of  attention 
which  so  costly  a  structure  as  an  iron  bridge  warrants. 
Too  often  insufficient  painting  is  allowed  to  remain  as 
the  only  protection  for  years,  the  fast-accumulating  rust 
either  not  being  noticed,  or  is  not  seen,  owing  to  the 
peculiar  color  of  the  paint  which  may  have  been  used. 
Because  a  bridge  is  an  iron  one,  it  does  not  imply  that  it 


80  IRON    HIGHWAY    BRIDGES. 

requires  no  further  care  after  it  is  once  finished*.  When 
iron  is  neglected,  it  is  only  a  question  of  time  as  to  its  final 
destruction.  A  large  bar  will  rust  out  only  less  rapidly 
than  a  small  one,  or  a  thick  plate  than  a  thin  one,  and 
there  are  circumstances  of  location  that  will  cause  rust- 
ing to  proceed  with  varying  rapidity.  It  is  with  a  view 
to  permanence  of  iron  structures  that  it  is  recommended 
in  no  case  to  allow  of  plates  or  parts  to  be  used  less  than 
one  quarter  of  an  inch  in  thickness,  and  perhaps  five  six- 
teenths of  an  inch  would  be  still  more  desirable  as  a 
minimum  thickness.  It  is  further  advisable  to  have  iron 
bridges  so  designed  that  all  parts  of  the  work  should  be 
open  to  inspection,  and  within  reach  of  the  paint-brush. 
When  not  so  designed,  concealed  surfaces  should  be  her- 
metically sealed,  so  that  by  no  possibility  can  moisture 
find  its  way  within  to  work  a  sure  destruction.  Town 
authorities  should  insist  upon  more  care  being  exercised 
at  the  construction-works,  in  preparing  iron  for  shipment, 
than  is  usually  given  to  such  matters,  particularly  in 
times  of  close  competition,  when  the  profit  of  a  con- 
tractor is  made  up  from  small  economies.  This  extra 
care  will  amply  repay  the  very  small  addition  to  the 
price  that  it  would  necessitate. 

At  the  manufactory,  each  individual  piece  can  be  ex- 
amined and  protected  with  a  care  impossible  to  exercise 
after  the  parts  are  all  assembled  in  position  at  their  final 
location.  All  new  iron,  as  it  comes  from  the  rolling-mill, 
has  a  scale  on  its  surface  easily  detached  under  vibra- 
tion. More  or  less  falls  off  while  it  is  undergoing  fabri- 


PAINTING    OF    IRON-WORK.  8 1 

,    § 

cation  into  shape,  but  enough  usually  remains  on,  to 
render  ineffective  the  paint  with  which  it  may  be  coated. 
This  scale  should  be  thoroughly  removed  at  the  shop  by 
scraping,  or  with  wire  brushes,  after  which  a  priming  coat 
will  take  hold.  Some  authorities  recommend  that  before 
scraping  off  the  scale,  the  iron  should  be  allowed  to  rust 
slightly,  as  giving  a  better  hold  for  the  paint.  In  any 
case,  the  paint  should  be  thoroughly  well  rubbed  into  the 
surface,  and  the  boiled  oil  and  turpentine  with  which  it 
is  mixed,  and  on  which  its  value  largely  depends,  should 
be  of  the  first  quality.  All  things  considered,  the  mineral 
paints  prepared  from  iron  ores  are  the  best  priming  paints, 
since  they  are  inexpensive,  and  therefore  unadulterated, 
which  can  not  be  said  of  many  of  the  red  leads  (a  favor- 
ite priming  paint  with  some  engineers)  in  the  market. 
Before  shipment,  iron  surfaces  that  have  had  machine-work 
put  upon  them,  called  bright  iron,  should  be  coated  with 
tallow,  to  which  a  body  of  white-lead  has  been  given. 
After  a  bridge  has  been  erected,  it  should  have  at  least 
two  coats  of  tinted  lead  paints,  care  being  taken  that  the 
brush  reaches  all  the  crevices  about  the  joints.  The  color 
of  the  final  coat  or  coats  had  better  be  of  such  a  tint  as  will 
show  the  first  indication  of  rust.  All  tints  bordering  on 
cream,  buff,  and  different  greys,  answer  this  purpose  excel- 
lently well ;  and  as  an  additional  advantage,  these  tints 
form  a  pleasing  and  appropriate  ground  for  decorative 
effect,  occasionally  required  for  first-class  city  bridges.  It 
is  recommended  that  all  iron  bridges  should  have  two  addi- 
tional coats  of  lead  paint  the  second  season  after  their 


82  IRON    HIGHWAY    BRIDGES. 

erection,  which  will  last  several  years  before  requiring 
renewal,  and  it  would  be  good  practice  for  the  authorities 
of  every  county  to  examine  their  bridges  systematically 
every  spring  for  signs  of  rust,  which,  if  discovered,  should 
be  attended  to  as  soon  as  possible.  In  this  way  their 
bridges  (if  originally  good  ones)  can  be  made  to  last  for- 
ever. 

THE    ARCHITECTURE   OF    BRIDGE- 
BUILDING. 

In  the  true  sense  of  the  term  architecture,  unadorned 
construction  is  as  much  a  part  of  architecture  as  the  more 
popular  idea  that  it  simply  covers  the  art  of  producing 
pleasing  effects.  A  man  can  not  be  a  good  architect  before 
he  is  a  good  constructionist,  no  matter  how  dextrous  he 
may  be  in  devising  graceful  forms,  or  artistic  in  his  selec- 
tion of  colors.  In  bridge-building,  there  is  little  room  for 
artistic  architecture,  and  any  pleasing  effect  produced 
must  grow  out  of  consistency  of  design,  and  a  thorough 
knowledge  of  the  peculiarities  of  materials  of  construction 
and  color.  To  an  educated  person,  correct  construction 
always  produces  a  sense  of  satisfaction,  for  in  it  is  involved 
the  idea  of  proportion  and  appropriateness  for  the  ser- 
vice to  which  it  is  put.  Concealment  of  constructive 
forms,  by  mouldings,  panels,  or  other  devices,  to  suggest 
something  else  than  what  the  construction  really  is,  is 
vulgar  as  well  as  dishonest.  To  construct  a  girder 
bridge,  and  give  it  the  appearance  of  being  an  arch,  il- 
lustrates what  is  here  meant  by  falsity  in  architecture, 





BRIDGE    ARCHITECTURE.  83 

specimens  of  which  more  than  one  of  our  public  parks 
contain.  Possibly  to  bridges  more  than  to  any  other 
class  of  public  works  does  the  Ruskinian  axiom  (which 
can  not  be  repeated  too  often)  apply :  "  Decorate  the 
construction,  but  not  construct  decoration."  Such  a 
principle  conscientiously  kept  in  view  can  not  but  result 
in  else  than  good  work.  Its  violation  results  in  a  sense- 
less fraud,  demoralizing  to  the  taste  of  the  community 
where  such  violations  may  occur.  Public  works,  in  a 
certain  sense,  play  a  part  in  the  education  of  a  people, 
and  their  authors  and  builders  have  consequently,  to  that 
extent,  a  responsibility  in  addition  to  the  mere  utilitarian 
idea  of  endurance  and  safety.  The  ideas  herein  ad- 
vanced are  not  novel  ones  by  any  means ;  but  they  can 
not  be  enforced  too  often,  when  in  this  boasted  age 
of  culture  and  civilization  a  community  will  permit  the 
huge  architectural  fraud  of  the  Fairmount  Bridge  over 
the  Schuylkill  at  Philadelphia,  and  hardly  yet  completed. 
Constructively,  this  bridge,  with  its  double  tier  of  floors, 
spanning  the  Schuylkill,  in  a  single  stretch  of  340  feet, 
is  a  monument  to  its  designer  and  an  honor  to  Ameri- 
can engineering.  Instead,  however,  of  letting  the  enor- 
mous trusses  stand  in  all  their  grandeur,  depending 
wholly  upon  judicious  painting  and  the  design  of  the 
cornices  and  railing,  etc.,  for  their  aesthetic  effect, 
thousands  of  dollars  have  been  spent  in  actually  cover- 
ing up  the  trusses  to  a  great  extent  with  sheet-iron,  form- 
ing an  arcade  as  it  were  of  great  massiveness,  by  arching 
between  the  posts  of  the  trusses,  the  arches  springing 


84  IRON    HIGHWAY    BRIDGES. 

from  large  Roman  sheet-iron  capitals  about  half  way 
down  the  posts !  The  result  is  that,  at  a  little  distance, 
the  spectator  beholds  an  arcade,  without  any  visible 
means  of  support  for  a  distance  of  340  feet.  To  be 
thoroughly  consistent,  the  architect  (heaven  save  the 
name !)  of  this  constructed  "  decoration  "  should  have  at 
least  sanded  his  sheet-iron  when  painted,  and  marked  out 
in  strong  lines  the  joints  that  masonry  of  similar  forms 
suggests.  About  one  mile  north  of  this  bridge,  a  noble 
structure  spans  the  Schuylkill,  the  Girard  Avenue 
Bridge,  as  it  is  called.  As  an  engineering  accomplish- 
ment, it  stands  in  no  comparison  with  the  bridge  at 
Fairmount,  the  spans  being  much  smaller,  and  only  a 
single  roadway  (of  paved  granite)  is  carried  on  the 
upper  chord,  it  being  a  "  deck-bridge."  Architecturally, 
it  is  certainly  one  of  the  finest,  if  not  the  very  finest, 
bridges  in  America ;  while  in  the  same  sense  the  Fair- 
mount  bridge  is  the  worst,  and  probably  the  worst  in 
the  world.  The  Girard  Avenue  is  an  example  of  pure 
decorated  construction,  and  the  writer  is  aware  of  no  place 
in  this  country  where  the  principles  for  \vhich  he  has 
been  contending  can  be  so  well  illustrated  as  in  the  case 
of  these  two  Philadelphia  bridges.  A  thirty-minutes' 
walk  will  carry  a  spectator  between  these  two  extremes 
of  very  good  and  very  bad  bridge  architecture. 

As  before  remarked,  a  truss-bridge  presents  little 
opportunity  for  architectural  effect,  further  than  what  is 
due  to  correct  construction,  and  the  taste  shown  in  the 
colors  with  which  it  is  painted.  In  a  through  bridge, 


BRIDGE    ARCHITECTURE    CONTINUED.  85 

•        § 

and  where  the  span  is  such  as  to  necessitate  a  depth 
of  truss  requiring  overhead  sway-bracing,  neat  corner- 
brackets  (either  of  wrought  or  cast  iron)  connecting  the 
vertical  posts  with  the  horizontal  struts  of  the  upper 
sway-bracing,  may  be  appropriately  introduced,  since 
they  act  as  knee-braces,  materially  stiffening  the  trusses 
against  vibration.  They  may  be  made  constructively 
useful  and  artistically  pleasing.  In  those  designs  involv- 
ing the  use  of  cast-iron  joint-boxes  between  the  upper 
chord  sections  and  posts,  these  boxes  may  be  cast  with 
neat  mouldings  and  necks,  forming  capitals  for  the  posts, 
in  any  conventional  architectural  forms.  The  effect  of 
such  caps  should  depend  entirely  on  the  strength  of  the 
mouldings,  and  not  on  detached  leaves  and  pieces 
screwed  on  after  the  casting  is  finished. 

When  trusses  terminate  in  vertical  end-posts,  there  is 
considerable  room  for  good  effect,  in  making  the  neces- 
sary stiffening  end  struts  or  portals  of  such  form  as  to 
embody  true  architectural  expression.  Such  a  design 
may  be  worked  out  either  in  cast  or  wrought  iron  with 
an  appropriate  degree  of  elaborateness.  In  doing  so, 
however,  the  main  lines  of  the  portal  must  form  an  in- 
tegral part  of  the  construction,  contributing  to  stiffness, 
and  any  appearance  of  brackets,  arches,  scroll-work,  etc., 
hanging  from  a  horizontal  strut,  must  be  avoided.  The 
capitals  of  end-posts,  when  vertical,  can  be  made  a  very 
prominent  feature  of  the  portal  design,  inasmuch  as  a 
large  casting  is  usually  required  at  the  juncture  of  the 
end-post  and  top  chord  to  accommodate  the  large  main 


86  IRON    HIGHWAY    BRIDGES. 

end-braces  terminating  at  that  point.  When  economy 
of  design  dictates  the  use  of  'inclined  end-posts,  the  por- 
tals will  produce  the  most  favorable  effects,  by  confining 
the  architectural  effort  to  the  expression  derived  from  the 
simple  bracing-bars.  An  arch-portal  of  angle  or  T  iron, 
with  the  spandrils  filled  in  with  lattice-work,  or  broken  up 
into  triangles  with  bracing-bars,  is  simple  and  expressive, 
and  exceedingly  appropriate.  The  lattice  intersections 
can  be  ornamented  by  small  rosettes  or  bosses,  and  the 
two  halves  of  the  portal-arches  can  be  united  properly 
with  a  half-circle  or  other  form  of  centre-piece,  while  at 
the  springing,  where  they  are  bolted  to  the  sides  of  the 
end-posts,  a  neatly-designed  bracket  or  shoe  will  not  be 
out  of  character.  It  is  exceedingly  difficult  to  design 
the  portals  for  inclined  end-posts  so  as  to  look  well,  since 
they  are  viewed  obliquely,  and  it  will  be  found  in  such 
cases  that  simplicity  of  design  growing  out  of  an  agree- 
able arrangement  of  constructive  necessities  will  always 
give  the  best  results.  The  appearance  of  a  roadway-bridge 
having  sidewalks  is  very  much  enhanced,  and  at  a  very 
small  cost,  by  neatly-designed  railings,  with  a  deeply- 
moulded  fascia-board,  to  which  may  be  added  scroll- 
drops  opposite  the  ends  of  the  floor-beams. 

It  is  not  necessaiy  that  such  railings  should  be  ex- 
pensive, a  light  lattice  railing  of  wrought-iron,  with  one 
or  more  intersections,  with  or  without  rosettes,  always 
looking  well  and  harmonizing  with  the  constructive 
character  of  a  truss.  The  cheap  gas-pipe  railing  is  so 
positively  ugly  that  its  use  ought  te  be  banished  to  those 


BRIDGE    ARCHITECTURE    CONTINUED.  87 

0 

country  districts  where  it  is  rarely  seen.  Well-designed 
newel-posts,  lamp-posts,  and  brackets  are  features  of  a 
design  where  a  cultivated  taste  may  be  exercised,  and 
form  no  small  part  of  the  prominent  accessories  of  public 
works  of  this  character.  This  matter  of  treating  bridge 
constructions  as  architectural  works,  in  the  true  sense  of 
that  term,  deserves  the  most  thoughtful  consideration  of 
engineers  and  committees,  as  bridges  nearly  always  form 
prominent  objects  of  observation  in  cities  and  towns, 
particularly  when  across  large  watercourses.  They  are 
seen  by  every  one,  and  therefore  in  those  portions  and 
surroundings  capable  of  aesthetic  treatment,  some  regard 
should  be  paid  to  appearances.  A  plain  four-walled 
building — as  a  court-house  for  example — might  answer 
every  requirement  for  public  purposes,  but  the  demands 
of  modern  civilization  require  that  a  large  expenditure 
must  be  made  for  what  is  called  "  architectural  effect,"  in 
order  that  a  certain  gratification  may  be  derived  by  the 
community  where  it  occurs,  springing  from  the  con- 
templation of  pleasing  forms.  Nothing  has  been  said 
about  masonry  design,  as  in  these  pages  we  are  simply 
dealing  with  the  superstructure,  but  as  the  masonry 
forms  part  of  a  bridge  design  when  taken  as  a  whole,  the 
form  of  piers,  abutments,  character  of  masonry,  coping, 
etc.,  it  must  not  be  forgotten,  leave  abundant  room  in 
many  cases  for  the  exercise  of  correct  aesthetic  treatment. 
There  are  very  few  who  can  not  appreciate  a  well-pro- 
portioned pier,  with  its  ice-breaker,  heavy  coping  and 
belting  courses,  well-laid,  rock-faced  work,  and  chisel- 
drafted  corners. 


88  IRON    HIGHWAY    BRIDGES. 

v 

TESTING. 

As  to  the  utility  of  testing  individual  pieces  of  work 
during  manufacture,  opinions  differ,  but  it  is  unquestion- 
ably a  wise  procedure,  in  the  case  of  welds  in  main  ten- 
sion bars,  as  imperfections  of  workmanship  and  material 
(if  any  exist),  undiscoverable  by  the  eye,  will  be  very  apt 
to  be  developed  under  strain.  To  avoid  injury,  it  is  ad- 
visable that  this  proving  should  not  be  carried  beyond 
say  nine  tenths  of  the  elastic  limit ;  thus  a  bar  with  an 
elastic  limit  of  20,000  Ibs.  per  square  inch  should  not  be 
tested  much  beyond  18,000  Ibs.  After  erection,  all 
bridges  should  be  tested  with  loads  approaching  as  near 
as  possible  the  maximum  loads  for  which  they  were  de- 
signed. Railroad-bridges  are  very  readily  tested,  but 
highway-bridges  can  only  be  tested  at  considerable  ex- 
pense. Pig-iron,  or  paving-blocks  when  convenient,  are 
probably  the  best  artificial  loads  that  can  be  used,  as  they 
are  readily  handled  and  distributed.  An  excellent,  though 
expensive,  method  of  testing,  and  one  of  universal  appli- 
cation, is  to  distribute  gravel  in  a  uniform  layer  over  the 
whole  area  of  roadway,  and  of  such  thickness  as  to  equal 
the  load  which  the  bridge  was  designed  to  carry.  Inas- 
much as  the  weight  of  gravel  and  earth  varies  according 
to  locality  and  degree  of  moisture  when  excavated,  before 
a  proposed  test  is  made,  a  cubic  foot  of  the  testing  mate- 
rial must  be  weighed  to  determine  the  proper  thickness 
to  be  put  on  the  bridge.  In  order  to  judge  the  result 
properly,  means  must  be  used  to  measure  the  deflection 


TESTING    OF    BRIDGES.  89 

f 

of  the  structure  undergoing  the  test,  which  may  be 
done  by  observations  with  a  levelling  instrument,  or 
when  convenient  (as  in  most  cases)  by  planting  a  pole 
or  measuring-rod  alongside  of  the  span  at  the  centre,  as 
follows :  After  the  bridge  is  completely  finished,  and 
come  to  a  natural  bearing  under  its  own  dead  load,  ob- 
serve the  position  of  any  part,  say  the  lower  chord  at  cen- 
tre, with  reference  to  the  position  of  the  instrument  or 
measuring-pole.  Then  apply  the  test  load,  and  measure  the 
amount  of  deflection  caused  thereby.  Remove  ,the  test, 
and  observe  again  how  near  the  bridge  returns  to  its  first 
position.  This  it  will  do  if  the  bridge  is  well  built,  less 
a  small  fraction  due  to  that  peculiar  quality  of  wrought- 
iron  which  is  called  "  permanent  set,"  which  takes  place 
under  comparatively  very  small  strains.  The  set  here 
spoken  of  must  not  be  confounded  with  that  taking 
place  after  the  elastic  limit  is  reached,  but  simply  means 
that  the  various  parts  of  the  bridge  have  come  to  a 
working  bearing.  If  the  test  load  is  now  applied  for  the 
second  time,  as  it  always  should  be,  it  would  be  found 
that  the  deflection  would  be  precisely  the  same  as  it  was 
before,  under  the  first  test,  and  so  also  the  amount  of  re- 
covery after  the  load  was  removed.  To  make  a  real 
test,  this  second  application  of  the  load,  with  accompany- 
ing observations,  should  not  be  omitted.  To  illustrate  : 
suppose,  at  the  first  loading,  the  deflection  was  two 
inches,  on  its  removal  the  span  recovered  itself  within 
one  eighth  of  an  inch.  This  proportion  of  the  deflection 
is  permanent,  due  to  the  span  coming  to  its  bearing,  and 


9O  IRON    HIGHWAY    BRIDGES. 

will  forever  exist.  The  second  loading  would  now  pro- 
duce a  deflection  of  i£  inches  instead  of  2  inches,  as  at 
first,  the  total  i$  plus  \  of  an  inch  being  precisely  the 
amount  of  the  original  deflection.  Upon  removal  of  the 
load,  the  recovery  \vould  be  i  £  inches,  the  same  as  before. 
Bridges  ought  always  to  be  built  with  a  camber  or  up- 
ward curvature,  which  camber  at  a  minimum  should  not 
be  less  than  the  deflection  caused  by  a  maximum  load- 
ing. Beyond  this  the  amount  is  purely  a  matter  of  taste 
with  the  designer,  it  having  nothing  whatever  to  do  with 
the  strength  of  the  work.* 

BRIDGE-LETTINGS. 

In  the  matter  of  "  Lettings,"  it  frequently  happens, 
that  parties  with  the  best  intentions  make  mistakes 
against  themselves  in  their  award,  simply  from  ignorance 
of  what  they  really  do  want,  and  by  so  doing  are  apt  to 
work  an  injustice  toward  competing  parties,  that  is  pro- 
vocative of  suspicion  and  ill-feeling  all  around.  With  a 
view  to  aid  in  a  clear  understanding  of  how  bridge-let- 
tings  should  be  conducted,  in  order  to  secure  the  best  re- 
sults at  the  least  cost,  the  following  forms  of  invitation 
and  specification  have  been  prepared,  in  the  hope  that 
they  will  save  \vell-meaning  committeemen  much  per- 
plexity. 

While  the  forms  recommended  are  brief  in  expres- 
sion, they  cover  aH  the  salient  points  necessary  for  a  fair 
competition.  The  specifications  are  general,  and  should 

*  All  bridges,  besides  being  tested  for  deflection,  under  a  dead  load,  should 
be  tested  to  see  that  they  are  measurably  free  from  vertical  and  lateral  vibra- 
tion, owing  to  lack  of  counter  and  horizontal  bracing.  The  best  test  for  this 
purpose,  is  to  have  a  couple  of  heavily  loaded  carts  driven  rapidly  back  and 
forth  over  the  roadway. 


THE    CONDUCT    OF    BRIDGE-LETTINGS.  91 

0 

be  made  so,  as  the  best  work  is  obtained  by  permitting 
bridge-builders  to  have  full  latitude  of  design,  under  no 
other  restriction  than  that  of  requirements  and  material. 
These  should  be  made  so  clear  that  no  refuge  for  evasion 
may  be  found  under  technicalities.  To  make  a  just  com- 
parison of  prices,  competing  parties  must  estimate  upon 
precisely  the  same  basis,  or  endless  confusion  will  result 
in  any  effort  to  make  a  fair  canvass  of  tenders.  It  is  re- 
commended, in  all  cases  of  a  bridge-letting,  to  call  in  the 
services  of  an  expert—not  simply  a  general  engineer,  but 
one  familiar  with  the  science  and  practice  of  bridge- 
building,  for  the  purpose  of  examining  the  strain-sheets 
submitted  with  the  tenders,  and  comparing  them  with  the 
specifications  on  which  bids  were  taken.  His  services 
should  be  continued  throughout  the  building  of  the  bridge, 
the  work  on  which,  however,  should  not  be  commenced 
before  all  detail  drawings  have  been  made  by  the  con- 
tractor, and  submitted  to  the  expert  for  criticism  and  ap- 
proval. If  it  is  inconvenient  to  employ  such  an  inspec- 
tor through  the  continuance  of  the  work,  he  should  be 
called  in  at  its  completion,  to  make  a  thorough  examina- 
tion as  to  the  material  and  execution,  in  accordance  with 
the  contract  and  specification.  A  suggestion  was  made 
in  a  report*  to  the  American  Society  of  Civil  Engineers 

*  Report  on  the  "  Means  of  Averting  Bridge  Accidents,"  by  James 
B.  Eads  ;  C.  Shaler  Smith,  of  St.  Louis  ;  I.  M.  St.  John,  of  Louisville  ; 
Thomas  C.  Clarke,  of  Philadelphia  ;  James  Owen,  Newark,  N.  J. ;  AIL 
P.  Boiler,  Octave  Chanute,  and  Charles  Macdonald,  New- York  ;  Julius 
W.  Adams,  of  Brooklyn,  and  Theodore  G.  Ellis,  of  Hartford,  Ct— 
Transactions  American  Society  Civil  Engineers,  1875. 


92  IRON    HIGHWAY    BRIDGES. 

on  the  subject  of  "  Bridge  Accidents,"  which  deserves  the 
very  serious  consideration  of  town  authorities.  It  was  to 
the  effect  that  every  bridge  built  should  have  a  tablet  fix- 
ed upon  it  in  a  conspicuous  place,  on  which  should  be  in- 
scribed the  name  of  the  builder,  the  expert  inspector,  the 
names  of  the  committee  or  corporation  officers  under 
whom  built,  the  load  for  which  it  was  proportioned  to 
carry,  with  factor  of  safety  and  date  of  erection.  Such  a 
method  of  procedure  tends  to  fasten  responsibility,  which 
is  a  powerful  incentive  to  honest,  conscientious  work,  and 
if  every  State  passed  a  law  covering  the  above  suggestion, 
there  would  in  a  short  time  be  a  surprising  improvement 
in  the  design  and  construction  of  highway  bridges,  al- 
though that  improvement  would  be  accompanied  with  an 
increased  cost. 

It  will  be  noticed,  in  the  last  clause  of  the  form  for 
"  Invitation,"  bidders  are  requested  to  be  present  at  the 
opening  of  the  bids,  and  hearing  them  read.  This  is 
simple  justice  ;  and  when  one  considers  the  time  required 
to  make  plans  and  estimates,  even  for  a  small  piece  of 
work,  to  say  nothing  of  the  expenditure  of  money  inci- 
dent thereto,  with  probable  travelling  expenses  in  addi- 
tion, no  fair-minded  man  can  object  to  rendering  at  least 
what  satisfaction  may  be  derived  from  the  public  opening 
of  tenders.  Bids  secretly  opened  always  lead,  whether 
justly  or  unjustly,  to  the  suspicion  of  unfair  practices,  an 
imputation  that  can  be  readily  removed  by  the  method  of 
publicity  suggested,  a  method  which  can  be  objected  to 


FORM    OF    INVITATION    AND    SPECIFICATION.  93 

0 

by  no  one,  unless  those  whose  mode  of  doing  business 
seeks  darkness  rather  than  light. 

PROPOSED    FORM    OF     INVITATION     TO    "  BRIDGE-BUILDERS. 


The  undersigned  committee  of  .................. 

will  meet  at  ..................  at  ....  o'clock,  on  the 

....  day  of  ......  ,  for  the  purpose  of  receiving  plans 

and  proposals  for  the  furnishing  of  all  material,  the  con- 
struction  and   erection   of  a  wrought-iron   bridge  over 

......................  ,  agreeably  to  the  specifictions 

hereto  annexed.  Parties  tendering  must  furnish  a  clearly 
made-out  strain-sheet  of  their  design,  with  the  data  on 
which  it  was  computed,  and  showing  also  the  areas  of  ma- 
terial proposed  to  be  given  to  each  part.  Bidders  are 
requested  to  be  present  on  the  above  occasion,  when  all 
the  proposals  will  be  opened  and  read  in  their  presence. 
The  right  to  reject  any  or  all  bids  is  reserved. 
Signed  by  the  Committee, 


PROPOSED    FORM    OF      STANDARD    SPECIFICATION     FOR    OR- 
DINARY   HIGHWAY    BRIDGES,  WHEN    INVITING    TENDERS. 

GENERAL  DESCRIPTION. — The  bridge  will  be  a 
(through  or  deck)  bridge,  consisting  of  ....  spans,  and 
will  have  a  roadway  of  ....  feet  between  guards,  with 
....  sidewalks  of  ....  feet  in  the  clear  each.  Sidewalks 
to  be  raised  ....  inches  above  level  of  roadway. 

The  distance  from  grade  to  bed  of  stream  (or  from 


94  IRON    HIGHWAY    BRIDGES. 

grade  to  grade  of  roads  crossing  each  other)  is  ....  feet. 
From  grade  to  highest  water  is  ....  feet,  and  the  centre 
line  of  the  bridges  makes  an  angle  of  ....  degrees  (to 
the  right  or  left),  with  the  face  of  abutment  or  piers. 

LOADS  TO  BE  CARRIED. — The  bridge  must  be  propor- 
tioned to  carry,  in  addition  to  its  own  weight,  ....  Ibs 
per  square  foot  (see  table,  page  16)  of  moving  load, 
starting  at  one  end,  and  moving  over  until  the  whole 
span  is  covered,  in  addition  to  which  the  flooring  system 
must  be  proportioned  to  carry  ....  tons  (of  2000  pounds) 
on  each  pair  of  wheels  for  each  wagon-way,  and  due  con- 
sideration must  be  given  to  the  effect  of  this  concen- 
trated loading  upon  the  posts  and  tension-braces  of  the 
trusses.  The  stringer-beams  and  floor-beams  (to  be 
wood  or  iron,  as  desired). 

FACTOR  OF  SAFETY. — Under  the  above  loading,  the 
factor  of  safety  referred  to  Ultimate  strength,  shall  be  for 
the  chords  (4  or  5),  for  the  web  system  5,  and  for  all 
parts  of  the  floor  system  (5  or  6). 

MATERIAL. — The  wr ought-iron  used  shall  be  of  that 
quality  best  suited  to  the  purpose,  the  test  for  bars  being 
that  pieces  cut  therefrom  shall  be  capable  of  being  bent 
cold  without  fracture,  until  the  two  sides  of  the  bend 
shall  approach  each  each  other  within  the  thickness  of 
the  bar.  No  iron  in  small  bars  to  be  used  with  an  ulti- 
mate strength  of  less  than  55,000  pounds  per  square  inch, 
or  an  elastic  limit  of  less  than  24,000  pounds  per  square 
inch.  Castings  must  have  a  clean  skin,  free  from  holes 
or  cinder  and  expose  when  broken  a  fine-grained  grey 


CONSTRUCTION.  95 

0 

fracture.  Lumber  must  be  of  a  good,  merchantable  qua- 
lity, sound  and  free  from  black  or  loose  knots  and 
wind-shakes,  and  not  have  sap  on  more  than  three  cor- 
ners for  planks,  or  on  two  for  stringer-timbers,  or  wany 
edges  on  more  than  one  corner.  For  roadway  plank  the 
lumber  will  be  of three  inches  thick,  for  side- 
walk plank,  two  inches  thick  of ,  and  for  string- 
ers   pine  will  be  required. 

CONSTRUCTION. — In  pin-connection  designs,  the  pins 
must  be  carefully  turned  to  match  the  holes  of  the  seve- 
ral parts  of  the  trusses  through  which  they  pass,  with  a 
minimum  play  of  a  scant  -fa  of  an  inch,  and  in  diameter 
must  not  be  less  than  T8¥  the  width  of  the  largest  bars 
they  connect,  if  of  flat  iron,  or  if  the  bars  are  of  square 
iron  the  diameter  must  not  be  less  than  if  times  the 
side  of  the  largest  square.  The  heads  of  eye-bars  must 
have  at  least  50  per  cent  of  effective  section  more  than 
in  the  body  of  the  bar.  The  bearing  surfaces  of  the 
compression  members  on  the  pins  must  be  effectively  re- 
inforced, so  that  the  minimum  thickness  in  inches  of  such 
surface  will  not  be  less  than  the  result  derived  by  divid- 
ing the  maximum  strain  as  shown  on  the  strain-sheet 
in  pounds,  by  12,000  times  the  diameter  of  the  pin. 
All  bearing  surfaces  must  be  machine-faced,  and  any  dis- 
crepancy in  length  between  all  parts  in  the  same  panel 
must  not  exceed  TaT  of  an  inch.  Where  rivets  are 
used,  serving  to  transmit  strain,  and  not  simply  for  the 
purpose  of  securing-  parts  in  position,  they  should  be  pro- 
portioned as  to  number  and  size  by  considering  the  work- 


96  IRON    HIGHWAY    BRIDGES. 

ing  value  of  each  rivet  to  be  equal  to  its  diameter,  mul- 
tiplied by  12,000  pounds,  multiplied  by  the  thickness  of 
the  thinnest  plate.  The  plates  and  angle-bars  subject  to 
tension,  under  such  riveted  construction,  must  have  an 
allowance  made  up  for  the  area  cut  out  by  the  rivet-holes. 

Pin-connection  work  and  solid  section  iron  will  be 
considered  to  have  an  advantage  of  10  to  20  per  cent 
over  and  above  riveted  or  compound  work.  The  spac- 
ing of  the  rivets  must  not  exceed  five  inches  between 
centres,  and  in  the  flanges  of  plate-girders  this  pitch 
must  be  reduced  as  the  ends  are  approached,  according 
to  the  value  obtained  by  the  above  rule  for  the  propor- 
tioning of  rivets.  Before  shipment,  all  iron  must  have  a 
thorough  coating  of  mineral  paint,  well  rubbed  in,  and 
all  bright  work  must  be  protected  with  white-lead  and 
tallow. 

To  the  above  specifications  must  be  added  the  degree 
of  finish  required,  such  as  the  painting  after  erection,  the 
manner  in  which  sidewalk  is  to  be  laid,  whether  the  plank 
is  to  be  planed,  etc. ;  also  the  kind  of  railing  desired, 
whether  plain  or  ornamental,  and  proposed  arrangements 
for  lighting. 


^: 


OP  THE 

UHI7BRSIT7 


PART   II. 

THE   STRAINS   IN   GIRDERS  AND   SIMPLE 

TRUSSES. 

ALL  questions  involved  in  the  consideration  of  this 
subject  resolve  themselves  into  mere  questions  of  lever- 
age, of  greater  or  less  complexity.  It  is  by  means  of  the 
law  of  the  lever  that  we  are  enabled  to  determine  pre- 
cisely what  portion  of  a  given  weight  resting  on  a 
beam  is  sustained  by  either  point  of  support,  which  is 
the  first  thing  to  be  determined  before  the  strains  can  be 
computed.  The  law  is  simply  this :  "  The  weights  bal- 
ancing each  other  at  either  end  of  a  beam  or  lever  over 
any  point,  are  to  each  other  inversely  as  their  distances 
(called  lever-arms)  from  the  point  or  fulcrum."  For  ex- 


i * "- t 


FIG.   24. 


ample,  supposing  we  have  a  beam  held  up  as  in  Fig.  24, 
with  a  weight  at  either  end,  the  point  of  support  be- 


Q8  IRON    HIGHWAY    BRIDGES. 

ing  to  one  side  of  the  centre,  say  at  J  the  length  of 
the  lever  from  one  end.  Then,  in  order  that  the  lever 
be  balanced,  the  weight  at  B  must  be  J-  the  sum  of  A 
and  B,  and  that  at  A,  £  that  sum ;  for  always  B  multi- 
plied by  |  S  must  equal  A  multiplied  by  i  S,  and  the 
sustaining  force  P  must,  of  course,  equal  the  sum  of  A 
and  B.  For  example,  suppose  P,  or  A  plus  B,  is  1 2  tons, 
and  the  span  S  is  20  ft.  For  equilibrium,  the  proportion 
of  the  1 2  tons  at  A  is  in  excess  of  that  at  B,  precisely  in 
the  proportion  that  the  lever  of  B  exceeds  that  of  A — 
in  this  case,  3  times.  A,  then,  must  be  9  tons,  and  B  3 
tons,  and  J  S  multiplied  by  9  equals  45,  being  the  same 
as  f  S  multiplied  by  3.  Again,  supposing  that  there  is 
but  one  weight,  and  two  points  of  support,  as  in  the 


r» 
...............       *     ......................  1 

lllllllllllllllllllllllllllllllllllllllllllHllltllllUlllllllilW 


FIG.   25. 

figure,  the  condition  is  precisely  the  same  as  before,  only 
reversed,  and,  according  to  the  law  of  the  lever,  we  find 
that  for  equilibrium  a  force  must  be  applied  to  A  equal 
to  |  of  P,  and  at  B  equal  to  J-  P.  This  last  example  is 
precisely  the  same  case  as  that  of  a  beam  or  truss  of  any 
kind,  only  A  and  B  are  now  called  the  reactions  of  the 
abutments,  the  sum  of  which  must  always  be  equal  to 
the  weight  or  weights  causing  them.  In  order  then  to 
know  just  how  much  of  the  weight  at  any  point  of  a 


ABUTMENT    REACTIONS PRINCIPLE    OF    MOMENTS.       99 


• 


beam  is  supported  by  either  abutment,  all  that  is  neces- 
sary to  be  done  is  to  multiply  the  shorter  or  longer  seg- 
ment into  which  its  centre  of  gravity  divides  the  beam 
(according  to  the  above  law)  by  the  weight,  and  then 
divide  by  the  product  by  the  sum  of  the  segments,  which 
is,  of  course,  the  same  as  the  span.  For  example,  sup- 


...  20 

FIG.    26. 


pose  we  have  a  beam  A  B  (Fig.  26)  20  ft.  long,  and  there 
is  a  weight  of  12  tons,  J  the  distance  from  B,  or  5  ft. 
Then  each  abutment  supports  or  "reacts"  a  certain 
amount  of  this  weight  proportional  to  its  distance  from 
either  end,  the  sum  of  these  reactions  being  equal  to 
the  weight.  A  supports  or  reacts  according  to  the  rule : 

12  tons  x  5  ft.  ,   -r,  12  tons  x  15  ft. 

i5ft.  +  5ft.-==  3  tons;  and  B  supports  -I5-ft.+  5ft.  =9 tons- 
Adding  these  two  upward  reactions,  there  results  a  total 
of  1 2  tons,  the  same  as  the  whole  load  at  P  acting  down- 
ward. Any  number  of  weights  are  to  be  treated  in  the 
same  way,  the  sums  of  their  separate  reactions  being  the 
total  reactions  or  weight  supported  at  each  abutment 
Any  weight  or  force  multiplied  by  the  leverage  at  which 
it  acts  is  called  the  moment  of  that  weight  or  force.  The 
leverage  or  lever-arm  of  any  force  is  the  perpendicular 
distance  let  fall  from  the  point  around  which  its  moment 


100 


IRON    HIGHWAY    BRIDGES. 


is  taken  (or  the  "fulcrum")  upon  the   direction  of  the 
force.     Thus  if  we  have  a  force  P  (Fig.  27),  and  the  ful- 


FIG.    27. 

crum  about  which  it  acts  is  A,  then  /  is  the  lever-arm  of 
that  force,  and  P  multiplied  by  /  the  moment.  Since  the 
tendency  of  a  force  acting  with  a  lever  is  to  produce 
motion,  and  it  being  evident  that  all  the  forces  acting 
at  any  given  point  of  a  beam  or  truss  can  not  act  in 
the  same  direction,  it  follows,  if  equilibrium  is  to  be 
maintained,  the  sum  of  all  tendencies  to  move  in  one 
direction  must  equal  those  in  the  opposite  direction,  or 
their  algebraic  sum  be  zero. 

The  ordinary  crowbar  (Fig.  28)  is  a  familiar  eve,ry- 


FIG.  28. 


day  example  of  the  "  principle  of  moments"  above  ex- 
plained. Suppose  a  man  presses  down  with  a  force  of 
loo  Ibs.,  distant  4  ft.  from  the  fulcrum  A.  The  moment 


ACTION  OF  FORCES  ON  A  BEAM.         IOI 

9 

of  this  pressure  is  100  Ibs.  multiplied  by  4  ft,  or  400  feet- 
pounds,  as  it  is  called,  and  it  acts,  with  reference  to  the 
fulcrum,  toward  the  left.  The  weight  that  will  just 
balance  this  moment  acts  toward  the  right,  with  a  lever 
of  6  inches,  or  one  half  a  foot ;  and  since  the  moment  of 
this  weight  must  equal  the  moment  of  the  pressure,  the 
weight  itself  must  be  800  Ibs.  For  800  Ibs.  multiplied 
by  one  half  of  a  foot  equals  100  Ibs.  multiplied  by  4  ft. 
To  absolutely  move  or  destroy  the  equilibrium  of  a 
weight  of  800  Ibs.  circumstanced  as  above  would  require 
the  man  to  just  exceed  a  pressure  of  800  Ibs.,  barring  the 
resistance  due  to  friction. 

In  any  beam  or  truss,  there  are  two  sets,  as  it  were,  of 
forces  in  action,  called  exterior  and  interior  forces ;  one 
tending  to  break  the  beam  through  bending,  and  the 
other  tending  to  resist  breakage.  The  former  are  de- 
rived from  the  weight  of  the  beam  and  the  loads  placed 
upon  it,  and  the  other  from  the  resistance  of  the  mate- 
rial, in  which  is  involved  the  form  of  cross-section. 
When  a  beam  is  bent  by  the  imposition  of  a  load,  it  is 
accompanied  with  a  pulling  apart  of  the  fibres  on  the 
convex  side,  and  a  crowding  together  of  those  on  the 
concave  side.  The  one  signifies  tension,  and  the  other 
compression,  and  in  passing  from  one  extreme  to  the 
other,  there  must  necessarily  be  a  set  of  fibres  without 
strain.  Where  these  unstrained  fibres  occur  is  called  the 
neutral  axis  of  the  beam,  and  its  position  is,  in  all  cases 
when  the  load  is  vertical,  in  the  centre  of  gravity  of 


IO2 


IRON    HIGHWAY    BRIDGES. 


the  beam-section.     The   annexed  illustrations  (Figs.    29 
and    30)  show  in   an  exaggerated   way   this   extension 


„.„. UNLOADED. 


LENGTHENED 
FIG.  29. 


FIG.    30. 

and  shortening  of  the  fibres,  and  it  will  be  noticed  that 
the  fibres  lengthen  or  shorten  proportionately  to  their 
distance  from  the  neutral  axis.  The  relative  intensity  of 
the  strain  is  also  measured  by  the  relative  changes  in 
length  of  the  fibres.  At  the  neutral  axis,  the  fibres  being 
unchanged  in  length,  there  is  no  strain ;  but  on  the  ex- 
terior surfaces,  the  top  and  bottom  of  the  beam,  the 
fibres  are  lengthened  or  shortened  a  maximum  amount, 
and  the  strain  is  there  a  maximum.  In  further  illustra- 
tion of  this  principle,  suppose  there  is  a  rectangular  beam 
(Fig.  31)  of  which  A  B  C  D  represents  a  side  view,  with 
the  neutral  axis  M  N  passing  through  the  centre  of 
gravity.  When  the  beam  is  loaded  with  a  weight  W,  it 
will  deflect,  due  to  the  shortening  or  compressing  of  the 
fibres  on  the  upper  surface,  and  lengthening  those  on  the 


STRENGTH  OF  BEAMS  OF  RECTANGULAR  SECTION.  1 03 

0 

lower,  as  before  explained.  Let  a  b  and  a'  b'  represent 
the  extreme  changes  in  length  of  the  fibres  on  the  outer 
surfaces.  Then,  since  the  strain  at  centre  is  nothing,  if 

W 


we  draw  two  triangles  either,  way  from  the  centre  to  the 
points  of  extreme  strain,  the  strain  on  any  fibre  will  be 
represented  by  the  length  intercepted  by  the  sides  of  the 
triangles  aO  and  6Q  and  a'O  and  b'Q. 

Summing  the  changes  of  length  of  all  the  fibres  in 
either  triangle,  there  results  the  representation  of  the  to- 
tal amount  of  the  tensile  and  compressive  strains,  or, 
what  is  the  same  thing,  the  sum  of  the  strains  may  be  re- 
presented by  the  areas  of  the  triangles,  their  mean  effect 
taking  place  at  the  fibres  of  mean  length,  or  the  centres 
of  gravity  of  the  triangles,  which  is  one  third  their  height 
from  their  bases,  or  two  thirds  the  distance  above  or  be- 
low the  neutral  axis.  This  mean  effect  is  represented  in 
the  figure  by  the  forces  P  and  P7.  These  two  forces, 
acting  in  opposite  directions,  and  parallel  to  each  other, 
constitute  what  is  called  a  couple,  their  leverage  of 
action  being  their  distance  apart,  which  lever  is  also  the 
effective  depth  of  the  beam.  To  determine  the  resistance 
of  a  rectangular  cross-section,  let  C  equal  stress  on  out- 


IO4  IRON    HIGHWAY    BRIDGES. 

side  fibre  represented  by  ab  or  a'b',  d  —  depth  of  beam, 
and  let  the  width  of  beam  be  taken  as  unity.  Then  from 
what  has  preceded  we  have  the  average  force  P  or  P' 
(equal  to  the  areas  of  either  triangle  or  \  C  X  k  d  =  P) 
multiplied  by  the  leverage  of  action,  or  the  distances 
apart  of  the  centres  of  gravity  of  the  triangles.  That 
is  to  say,  P=£  Cxi  dx^d—^  C  d\  For  any 
breadth  b  other  than  unity,  this  expression  becomes 

•p b  d*  f^ aiea  of  cross-section  \y     j  r^  /    \ 

r  —  "6~^—  ~  ~<T~  -;AtfV/ (I) 

This  is  a  general  expression  for  the  resistance  of  any 
beam  having  a  rectangular  cross-section,  and  is  called 
the  moment  of  resistance  of  the  cross-section  (usually 
designated  by  the  letter  R).  When  this  value  equals 
that  due  to  the  weight  multiplied  by  its  leverage 
of  action,  called  the  moment  of  rupture,  or  M,  there  is 
perfect  equilibrium  between  the  rupturing  and  resisting 
forces,  or,  in  algebraic  expression,  "  M  "  =  "  R." 

The  constant  C  is  called  the  modulus  of  rupture,  and 
were  it  not  for  certain  discrepancies  that  occur  in  the  re- 
sistance of  material  when  subjected  to  direct  compression 
or  tension,  and  to  cross  breaking,  its  value  would  be 
given  experimentally  by  the  force  necessary  to  tear  apart 
or  compress  a  bar  of  a  given  material.  It  is  unnecessary 
in  this  place  to  point  out  what  these  discrepancies  are, 
but  simply  the  fact.  Professor  Rankine  recommends 
that  the  value  of  C  for  any  kind  of  material  be  deter- 
mined by  taking  eighteen  times  the  force  necessary  to 
break  with  a  centre  load  a  bar  one  inch  square,  placed 


BEAMS  UNDER  DIFFERENT  CONDITIONS  OF  LOADING.  105 


on  supports  one  foot  apart*  Bearing  in  mind  the  prin- 
ciple of  the  equality  of  moments  of  rupture  and  resist- 
ance necessary  for  perfect  equilibrium,  as  previously 
explained,  the  following  application  to  beams  differently 
circumstanced  will  cover  the  requirements  of  ordinary 
practice. 

Beam   loaded    at    one  end,  fastened    at  /  s 

<$(* " •*• 

the  other.     Maximum  moment  of  rup-  '^_ 

ture  occurs  at  point  of  support.  The 
lever  which  produces  this  is  the  length 
of  the  beam,  or/.  FIG'  32< 

T3 

Mmax  =  W/  =  R  andW  =  — ••••(2) 

Beam    supported  at   one   end,  and    uniformly 

loaded  with   w   units  per  foot  ;    ivl  will  be      ^  • " -v 

therefore  the  total  load,  the  centre  of gravi-     ^LL>i- _•+•  l-l^-l-l-l^lHl^ 

,/    7 

ty   of  which  is   in    the   middle   of  beam,  or      %* tiJx. — >!  ^ ! 

leverage  of  action  to  produce  mean  moment 

FIG.  33. 
of  rupture  is  \  /. 

/        wl*  2R 

-w  X—--—-  "71" '3' 

Beam  loaded  at  centre  with  W,  and  sup-  i/2  w                   w  >/2  w 
ported  at  both  ends,  length   /.      Lever- 
age of  action  \  /for  the  reaction  of  either                                 k // 

abutment,  the  fulcrum  being  immediate-  / 

ly  under  the  weight.  FIG-  34' 

/     W/        _  ,     .__         4R 

Mmix  =  |W  x  i/==—  =  R    and    w=  y- (4) 

Beam  uniformly  loaded  with  w  per  unit 

of  length,  giving  wl  for  total   load —       9fiv\ wl --'A 

supported  at   both  ends.      Maximum  iiliiiiiiiiill 

moment  under  centre  gravity  of  load,          ^ -/2  I — »i 

v  ^...... .......   7    '      —.-----. -..^  jy  y/ 

lever  i  /.     Reaction  of  either  abutment 

FIG.  35. 
•^  the  whole  load. 

Mmax  =  -!-«//  X  i/less  \  wl  X  i  /  _  wl^_ ^._^_  R     nd 

~~~A~'        8     ""    8  a 


*  The  value  eighteen  times  the  breaking  force  used  in  determining  constant  C 
is  derivable  as  follows — see  Fig.  34 : 

Let  W  =  breaking  weight  at  centre  of  bar. 

C  =  required  constant  or  modulus  of  rupture,    (Continued  on  page  106.) 


IO6  IRON    HIGHWAY    BRIDGES. 

It  will  be  noticed  this  last  expression  is  obtained  by 
subtracting  that  portion  of  the  load  between  the  abut- 
ment and  centre  that  acts  in  a  contrariwise  direction  to 
the  reaction  of  the  abutment. 

If  the  loads  are  placed  in  any  other  position,  or  are 
only  partial,  M  can  always  be  found  by  first  finding  the 
reaction  of  either  abutment  (page  101),  and  multiplying 
that  reaction  by  the  distance  from  the  abutment  to  the 
point  where  M  is  wanted.  The  reaction  being  upward, 
if  there  are  any  weights  (which  act  downward}  between 
the  abutment  and  point  of  desired  M,  they  must  be  mul- 
tiplied into  the  leverages  with  which  they  act  around 
that  point,  and  their  sum  deducted  from  the  product  of 
the  reaction  and  its  leverage  before  found.  This  is  the 
principle  that  had  to  be  applied  to  the  circumstance  of 
loading  shown  in  Fig.  35.  As  an  example  of  the  applica- 
tion of  these  formulae  :  suppose  in  all  cases  the  material 
is  a  pine  stick  10"  X  10"  X  10  feet  or  120  inches  long. 
We  require  to  know  the  breaking  load  under  each  con- 
dition of  loading,  C  being  7000  Ibs.  See  formula  (i)  : 

I0 


No.  2.  W  =      =   °°°6XX0X      -  97"  lbs.-hung  at 
one  end. 

per  H. 


neal  inch  =  19,440  Ibs.  uniformly  distributed. 

No.  4.   W  =  ^  =  4  x  TxXiaT  —  =  38'888    lbs'~ 
supported  in  middle. 

No.  5.  »=  «  =  8x7rx°r4ZXIO=  648  Ibs.  per  li- 
neal  inch  =  77,760  Ibs.  uniformly  distributed. 

The  bar  being  one  foot  long  between  bearings,  and  one  inch  square,  we  have 


the  moment  due  to  external  forces  i  W  X  i  span  —  3  W. 

'A 

6 


And  the  moment  due  to  internal  forces  R  =  — r-  C  =  £  C. 


Since  M  must  equal  R,  we  have 

|  C  —  3  W ;  or  C  —  18  W. 


PRACTICAL    APPLICATION    OF    FORMULA. 


107 


p 

Now,  assuming  a  safety  factor  of  five,  the  safe  load 
to  which  the  above  stick  should  be  subjected  would  be  : 

One  end  fixed,  the  other  free  ;  weight  at  free  end *944  Ibs. 

One  end  fixed,  the  other  free  ;  weight  distributed. 3888  Ibs. 

Both  ends  supported  ;  weight  concentrated  at  middle.     7777  Ibs. 
Both  ends  supported  ;  weight  uniformly  distributed. .  .  15,555  Ibs. 

It  will  be  noticed  from  this  example  that,  taking  the 
first  case  as  having  a  strength  of  one,  with  the  second 
condition  of  loading  and  support,  the  stick  will  sustain 
twice  as  much,  with  the  third  four  times  as  much,  and 
with  the  fourth  condition  eight  times  as  much.  The 
third  and  fourth  conditions  are  those  that  apply  to  the 
longitudinal  stringer-beams  of  a  bridge,  and  from  formu- 
las 4  and  5  has  been  computed  the  following  table  for 
different  spans  or  panel-lengths  and  depths  of  stringers, 
the  thickness  being  for  a  unit  of  one  inch.  The  modulus 
of  rupture  C  for  pine  has  been  taken  at  8000  Ibs,  with  a 
factor  of  safety  of  six. 

TABLE  GIVING  A  SAFE  CENTRE  WORKING  LOAD  IN  POUNDS 
FOR  ANY  DEPTH  OF  PINE  STRINGER  AND  A  UNIFORM 
WIDTH  OF  ONE  INCH. 

CLEAR  SPAN  IN  FEET. 


Inches. 

6  feet. 

8  feet. 

10  feet. 

12  feet. 

14  feet. 

16  feet. 

18  feet. 

20  feet. 

6 

8 
9 

10 
12 
14 

16 

443 
602 
787 
996 

333 

454 
593 
750 
927 

266 
363 

474 
600 

74i 
1067 

302 

395 
500 
617 
888 
1209 

338 

428 
529 
76l 
1036 

I-JCA 

375 
463 

666 
907 
118? 

411 

591 
805 
ICK2 

527 
717 
Q^8 

108  IRON    HIGHWAY    BRIDGES. 

For  safe,  uniformly  distributed  loads,  double  the 
loads  given  in  the  table. 

To  use  the  above  table,  the  weight  to  be  carried  in 
the  centre  of  a  given  span  is  first  determined,  and  then 
select  any  depth  for  the  beam,  and  follow  along  the  hori- 
zontal line  until  below  the  span  at  top  of  column.  The 
number  there  found  will  be  the  safe  load  in  pounds  for  a 
beam  of  the  given  depth  and  one  inch  thick.  Divide 
the  weight  to  be  carried  by  the  number  of  pounds  found 
from  the  table,  as  above,  and  the  result  will  be  the  width 
in  inches  required  for  the  beam.  Thus,  for  example,  it 
is  required  to  know  how  thick  a  piece  of  timber  should 
be  that  is  10  inches  deep,  spanning  12  feet  to  carry  3000 
Ibs.  hung  in  the  middle,  or,  what  is  the  same  thing,  6000 
Ibs.  uniformly  distributed.  Opposite  10  in  the  first  col- 
umn and  below  1 2  in  the  fifth  column,  we  find  6 1 7  Ibs., 
the  safe  load  for  one  inch  thick.  Dividing  3000  by  617, 
we  find  the  timber  should  be  a  shade  less  than  5  inches 
thick.  The  following  table  is  given  as  showing  judicious 
sizes  for  the  wooden  stringer-beams  for  the  various 
classes  of  bridges,  and  for  varying  panel-lengths.  In 
judging  this  table,  it  is  to  be  considered  that  the  standard 
wheel  loads  recommended  in  Part  I.  are  extreme,  and 
therefore  very  occasional,  so  that  a  much  lower  factor  can 
safely  be  used  for  such  loads.  Under  these  circumstances, 
if  the  stringers  are  of  good  timber,  they  can  safely  be 
proportioned  for  a  working  stress  of  1500  Ibs.  per  square 
inch. 


FLANGE-BEAMS. 


I09 


Span  or  panel-length. 

Size  Stringers  for 
City  Bridges. 

Size  Stringers  for 
Town  Bridges. 

Size  Stringers  for 
County  Bridges. 

8  feet  ,  

1    X    IO 

3     x  10 

7     v        Q 

4  x   10 

4XIO 

9   v    IO 

4    X     12 

^4   x    12 

3xii 

14 

4x13 

4X12 

^    X    12 

16 

4  x   14 

4x13 

4    X    12 

18            . 

4  X    K 

4      X    14 

A    X     [  •» 

20        

4  x  16 

4      X    1  5 

4X    I-l 

Thus  far  we  have  been  dealing  with  rectangular 
cross-sections ;  but  bearing  in  mind  the  explanation  made 
as  to  the  stresses  on  the  different  fibres  of  a  beam  with 
reference  to  the  neutral  axis,  it  will  be  at  once  seen  how 
wasteful  it  is  to  have  so  much  material  near  the  neutral 
axis,  where  it  is  of  so  little  service.  If  the  material  were 
so  disposed  as  to  be  principally  in  the  upper  and  lower 
portions  of  the  beam,  the  strength  of  the  beam  would 
be  largely  added  to.  With  wood,  other  than  a  rectangu- 
lar section  is  evidently  out  of  the  question ;  but  in  iron, 
the  true  form  for  the  most  economical  distribution  of 
material  is  a  necessity  in  practical  construction,  and  is 
readily  attained  by  concentrating  most  of  the  metal  in 
the  upper  and  lower  portions  or  the  "  flanges,"  the  stem  or 
web  being  just  stout  enough  to  properly  unite  them,  and 
to  resist  the  tendency  of  one  part  of  the  beam  to  slide 
vertically  or  horizontally  past  the  other  under  the  direct 
action  of  the  load,  called  the  shearing  tendency.  For 
example,  the  accompanying  cut,  Fig.  36,  represents  the 
vertical  shearing  tendency  of  a  load,  which  is  least  at  the 
centre  and  greatest  at  the  abutments,  as  each  section 
either  side  of  centre  must  take  up  the  shear  of  each 


I  IO  IRON    HIGHWAY    BRIDGES. 

preceding  one.     Solid  rolled  beams  are  manufactured  in 
this  country  from  4  inches  deep,  with  3-inch  section,  to 


FIG.    36. 

15  inches  deep,  with  2oinch  section.  Their  ordinary 
length  up  to  and  including  the  9-inch  beam  is  30  feet. 
The  beams  exceeding  9  inches  have  an  ordinary  length 
of  from  20  to  25  feet,  according  to  weight.  Beams  are 
often  rolled  beyond  the  commercial  ordinary  length  ;  but 
the  cost  of  extra  lengths  increases  very  rapidly  with  such 
excess. 

To  determine  the  "  Moment  of  Resistance  "  of  flanged 
beam  sections,  we  must  consider  first  the  resistance  due 
to  the  rectangular  web,  and,  secondly,  that  due  to  the 
flanges.  The  resistance  due  to  the  web  portion  has 
already  been  shown  to  be  equal  to  one  sixth  of  its  area 
multiplied  by  its  height,  being  the  same  as  a  rectangular 
section.  That  of  the  flanges  is  the  area  of  either  one 
multiplied  by  the  distance  apart  of  their  centres  of  gra- 
vity, which,  when  added  to  the  resistance  of  the  web, 
gives  the  total  resistance  of  the  section.  The  web 
should  not  be  taken  the  whole  depth  of  the  beam, 
but  only  from  flange  to  flange.  Thus,  suppose  we 
want  to  know  "  R  "  for  the  beam  proportioned  as  in  Fig. 
37: 


MOMENT    OF    RESISTANCE FLANGE-SECTIONS.        Ill 


<— 5  /N. 


FIG.  37. 


£  area  web  =             *  —  — —  multiplied  by  13"  equal  14  083 
Area  flange  =  s"  x  i  "  —  5"  multiplied  by  14"  equal  70.000 
Resistance  of  section  "  R  " 84.083 

The  quantity  thus  obtained  has  only 
to  do  with  the  shape  of  section,  the 
efficiency  to  do  work  being  dependent  on 
the  quality  of  the  material.  R  must  there- 
fore be  multiplied  by  a  coefficient  expressing  this  quality 
before  the  strength  of  the  beam  becomes  known.  For 
wrought-iron,  this  coefficient,  within  safe  limits,  varies 
from  10,000  to  15,000  Ibs.  per  square  inch,  depending 
upon  the  requirements  of  any  given  specification.  The 
above  process  for  obtaining  the  value  of  R  varies  so 
fractionally  from  absolute  truth  that  the  refinement  of 
calculation  to  obtain  mathematical  exactness  is  entirely 
unnecessary,  while  the  ease  of  its  application  is  so  great 
that  but  a  few  moments  of  the  simplest  arithmetical 
processes  are  all  that  is  required  to  compute  the  resisting 
value  of  any  beam  cf  the  usual  patterns. 

The  formulae  already  given  for  different  circumstances 
of  loading,  page  105,  may  be  divided  by  the  assumed 
maximum  strain  per  square  inch  allowed  on  the  iron, 
which  amounts  to  the  same  thing  as  multiplying  R  by 
the  same  quantity,  and  is  the  most  convenient  way  of 
introducing  the  above  coefficient.  As  an  example  in 
applying  the  above  principles  for  determining  the  proper 
size  of  beam  for  any  given  load,  let  us  take  the  condition 
of  loading  given  by  equation  5,  page  105.  Let  the  load 
to  be  carried  be  40,000  pounds,  uniformly  distributed, 


112 


IRON    HIGHWAY    BRIDGES. 


and  the  maximum  allowable  strain  be  10,000  Ibs.  per 
square  inch  ;  span,  15  feet,  or  180  inches.  Then  formula 
5  would  read : 

A/rmax         40,000  Ibs.  multiplied  by  180  inches  _    p  _ 

8  multiplied  by  10,000  Ibs.  per  sq.  in.  ~ 
A  beam  must  therefore  be  designed  having  this  value 
of  R,  precisely  as  described  on  page  in.  It  will  be 
noticed  that  the  section  there  computed  falls  a  little 
short  of  a  moment  of  90,  which  would  be  attained  by 
increasing  the  flange  areas  ten  per  cent.  Since  each 
beam- section  has  its  own  value  of  R,  the  following  table 
gives  this  value  for  all  shapes  of  "  Phoenix  "  beams,  and 
is  about  the  same  for  the  same  sizes  of  other  makers : 

TABLE    GIVING    THE    VALUE    OF    R    FOR    ALL    SECTIONS    OF 
AMERICAN    BEAMS. 


Total  depth 
in  inches. 

Weight  per 
foot. 

Area  of  one 
flange. 

Distance  be- 
tween cen- 
tres of 
flanges. 

Area  of 
stem. 

Depth  of  stem. 

Moment  of  re- 
sistance, 

R. 

15 

66* 

6.IO 

13.80 

7.80 

11.875 

IO2.20 

IS 

50 

4-312 

14.04 

6-375 

12.750 

75-44 

12 

561 

5-755 

IO.92 

5-49 

9.250 

72.85 

12 

4H 

3-790 

ii.  16 

4.92 

IO.OOO 

51.48 

10* 

35 

3-380 

9-74 

3-74 

8.625 

38.96 

9 

50 

5.50 

7.90 

4.00 

6.375 

48.70 

9 

28 

2.78 

8.30 

2.84 

7.000 

27.00 

23i 

2.37 

8.38 

2.26 

7.250 

22.88 

g 

2l£ 

2.035 

7.42 

2.43 

6.500 

18.11 

7 

1  8* 

i.  80 

6.44 

1.90 

5.500 

13-63 

6 

i6f 

1.82 

5.50 

1.36 

4.375 

11.25 

5 

12 

1.175 

4.60 

1.25 

4.000 

6.37 

5 

IO 

•995 

4.62 

1.  01 

4.063 

5.38 

4 

IO 

1.14 

3.58 

.72 

2.900 

4.50 

6 

•545 

3.65 

.71 

3.250 

2.45 

To  use  the  table,  compute  the  maximum  bending  moment  as  before 
explained,  and  select  the  beam  having  the  largest  value  of  R  nearest 
to  the  computed  one,  in  case  there  is  none  having  the  exact  required 
value. 


COMPOUND    GIRDERS.  1.13 

0 
COMPOUND     GIRDERS. 

For  beams  compounded  from  plates  and  angles,  the 
process  for  determining  R  is  precisely  the  same  as  for 
any  other  beam.  Inasmuch  as  compound  beams  are 
specially  designed  for  any  given  case,  it  is  necessary  to 
determine  from  R  the  area  of  the  flanges  and  web,  from 
which  the  proportions  of  the  parts  can  be  made  out.  It 
must  be  remembered  that  M  or  R  do  not  represent 
strain,  being  independent  of  depth,  but  can  be  converted 
into  flange  strain  by  dividing  by  the  depth  in  inches. 
Assume,  therefore,  any  depth  for  the  girder  (bearing  in 
mind  that  the  effective  depth  is  the  distance  between 
centres  of  gravity  of  the  flanges*),  divide  R  by  this  depth, 
and  the  result  is  the  strain  on  either  flange ;  and  if  the 
maximum  allowable  strain  per  square  inch  has  not 
already  been  introduced  in  determining  R,  the  strain 
above  found  must  be  divided  by  this  maximum  unit 
strain  to  determine  the  square  inches  that  must  be  .given 
to  the  flanges. 


*  To  find  the  centre  of  gravity  of  a  flange  com- 
posed as  in  Fig.  38,  and  representing  a  plate  web- 
girder,  assume  any  axis,  as  XY. 


Area  of  the  whole  flange  =  M  =  m  *  m. 

Let  /  equal  distance  centre  of  gravity  of  m  from  axis. 
.<  //     <i  <t  «  «  m'   " 

,«  x     .«          «  «  ••          M    " 

To  find  x. 


L 

I 

m 


ml  +  m't  FIG.  38. 

MX  =  ml  +  m?  and  x  = — 


114  IRON    HIGHWAY    BRIDGES. 

Taking  the  same  case  as  before,  it  is  required  to  know 
the  flange  area  of  a  compound  beam  15  feet  long,  15 
inches  deep,  with  a  half-inch  web.  The  load  being  40,- 
ooo  Ibs.  uniformly  distributed,  the  maximum  strain  to  be 
10,000  Ibs.  per  square  inch,  and  the  assumed  effective 

depth  13  inches.  Then,  by  formula  5,  f^°  p0^ *  13  =  6-92  • 
square  inches,  the  required  flange  area,  toward  which  the 
web  contributes  ^  of  its  area,  or  ^^  =1.25  inches,  leaving 
(6.92  less  1.25)  to  be  built  up  with  angle  irons,  5.67  square 
inches  section  net,  after  rivet-holes  are  deducted  for  the 
tension-flange — an  allowance  unnecessary  to  be  made 
for  the  compression  flange,  since  that  flange  is  not  weak- 
ened by  the  removal  of  metal,  if  filled  in  again  as  it  is 
with  the  rivets.  Since  it  is  customary  to  allow  a  less 
strain  per  square  inch  for  compression  than  for  tension, 
both  flanges  of  plate-girders  are  usually  made  alike,  the 
area  of  the  bottom  determining  that  of  the  top.  The 
allowance  for  rivet-holes  in  such  forms  of  plate-girders 
as  are  being  considered  is  about  1 5  per  cent,  and  adding 
that  amount  to  the  net  area  already  found,  the  gross  area 
of  the  angle  irons  must  be  6£  square  inches,  which  is 
given  by  two  angles  \  inch  thick,  and  legs  3^  inches 
4....?.:'....*  long,  To  check  the  effective  depth  as- 

sumed, we  have  (see  foot-note,  page  113)  : 


js      m  =  7"  x  i"=  3-5  inches;  m'=  3"  X  i"  = 
3  inches,  and  M  —  6.5" 

FIG.  39.  x  — 3  •5x°^  +  3x2  _  agog  inches  from  outer 


RIVETING    OF    COMPOUND    GIRDERS.  115 

edge  for  each  flange,  making  1.6 1 6  inches  as  the  amount 
that  the  full  depth  is  reduced,  or  15"  less  1.6 1 6  inches, 
equal  to  13.38  inches,  being  practically  the  same  as  the 
effective  depth  assumed. 

In  comparing  riveted  beams  with  solid  rolled  beams, 
it  must  not  be  forgotten  that  the  latter  are  at  least  10  per 
cent  stronger  than  the  former;  or,  in  other  words,  if 
10,000  is  the  unit  of  strain  selected  for  the  riveted  work, 
the  solid  beam  will  have  as  great  strength  if  propor- 
tioned for  a  unit  of  strain  of  1 1 ,000  Ibs.  per  square  inch. 

In  order  to  develop  the  full  strength  of  a  riveted 
beam,  due  to  the  section,  more  attention  should  be  paid 
to  the  riveting  than  is  usually  done,  as  to  number,  size, 
pitch,  and  method  of  driving.  The  duty  of  the  rivets  is 
to  take  up  all  the  horizontal  increments  of  strain  deliv- 
ered by  the  web  to  the  flanges.  The  horizontal  strains 
in  the  flanges  diminish  in  intensity  either  way  from 
position  of  maximum  M  at  centre,  toward  either  abut- 
ment, where  they  are  least,  and  may  be  found  at  any 
point  by  dividing  the  moment  at  that  point  by  the 
effective  depth.  The  horizontal  increments  of  the  web 


FIG.  40. 


are  greatest,  however,  at  the  ends,  and  least  under  posi- 
tion of  maximum  M.  This  can  be  made  clear  from  an 
inspection  of  the  accompanying  illustration  (Fig.  40), 


Il6  IRON    HIGHWAY    BRIDGES. 

where  A  B  represents  a  girder  loaded  uniformly.  The 
web  is  divided  into  four  imaginary  panels,  either  side  of 
centre,  and  the  horizontal  effect  of  each  panel  and  their 
summation,  as  the  centre  is  approached,  being  represented 
by  arrows.  The  relative  intensity  of  the  horizontal 
effect  is  indicated  by  the  varying  thickness  of  the  ar- 
rows. It  has  before  been  stated  that  the  value  of  a 
rivet  is  its  diameter  multiplied  by  the  thinnest  plate 
through  which  it  passes,  multiplied  by  the  working 
strain  per  square  inch.  In  the  case  of  a  plate-girder, 
this  thinnest  plate  would  be  the  web,  and,  assuming  such 
a  plate  f  inch  thick,  a  J  rivet  under  a  working  strain  of 
10,000  Ibs.  per  square  inch  would  have  a  value  of 
10,000  X  £"X  £  =  3300  Ibs.  If  the  maximum  horizontal 
strain  is  divided  by  3300  Ibs.,  there  results  the  minimum 
number  of  rivets  required  either  way  from  the  point  of 
such  strain.  Owing,  however,  to  the  greater  intensity 
of  the  horizontal  increments  of  strain  of  the  web 
toward  the  ends,  the  rivets  should  be  spaced  closer  as 
the  ends  are  approached.  Applying  these  rules  to  the 
girder  previously  computed,  the  loading  o£  which 
brought  the  maximum  strain  at  the  centre,  this  strain 
was  found  to  be  69,200  Ibs. ;  and  using  a  f-inch  web 
and  §  rivets  as  above,  we  find  that  the  number  of  rivets 
required  either  way  from  the  centre  to  the  ends,  a 
distance  of  90  inches,  will  be  (~jr)  about  2 1 ,  which,  if 
uniformly  pitched,  would  be  spaced  a  shade  over  4 
inches  between  centres.  It  will  be  better,  however,  for 
the  reasons  above  given,  to  use  more  rivets,  spacing 
them  3  inches  for  the  first  end  quarter,  or  for  45  inches, 


WEB-STIFFENERS.  I  i  7 

f 

the  balance  being  44  inches  pitch.  At  first  sight,  from 
theoretical  considerations  purely,  it  would  seem  that  a 
good  proportioning  of  riveted  work  would  require  a 
variation  in  size  of  rivets,  but  such  designing  would 
cause  endless  trouble  during  manufacture.  Uniformity 
of  parts  in  design  is  essential  to  economical  production, 
as  well  as  for  the  avoidance  of  shop  errors,  and  for  this 
reason,  in  flange-riveting,  the  same  size  rivets  should  be 
used  throughout,  and  change  of  pitch  avoided  as  much 
as  possible.  Some  manufacturers  depend  more  or  less 
upon  the  efficiency  of  rivets  being  increased  by  reason 
of  the  friction  of  the  rivet-heads  against  the  plates,  due 
to  their  shrinkage  after  being  driven.  There  is  no  doubt 
but  that  in  new  work  this  friction  is  very  great,  and  ma- 
terially aids  the  rivet,  but  as  it  is  uncertain  how  much 
this  is  impaired  after  a  long  term  of  service,  as  well  as 
the  variability  of  the  value  of  the  friction,  it  is  deemed 
by  the  most  prudent  designers  of  iron-work  to  make  no 
allowance  whatever  for  friction,  but  proportion  rivets 
only  with  reference  to  their  bearing  surfaces  and  shear- 
ing areas.  As  to  stiffeners  for  the  webs  of  girders  in 
highway  bridges,  they  are  unnecessary  if  the  thickness 
of  the  plate  is  such  that  the  unsupported  distance  be- 
tween the  legs  of  the  upper  and  lower  flange  angle  iron 
is  not  greater  than  from  35  to  40  times  that  thickness. 
If  this  proportion  is  exceeded,  stiffeners  must  be  intro- 
duced at  intervals  and  over  the  points  of  support.  Since 
the  floor-girders  of  a  highway  bridge-  are  proportioned 
(or  should  be)  for  the  extreme  standard  load,  the  rarity 
of  such  occurrence,  if  it  ever  really  occurs  at  all,  is  such 


n8 


IRON    HIGHWAY    BRIDGES. 


as  warrants  the  recommendation  of  a  unit  strain  of 
15,000  Ibs.  per  square  inch  to  be  used  for  the  net  section 
of  the  lower  flange.  Angle  and  plate  iron  can  now  be 
readily  obtained  of  a  good  quality,  with  elastic  limits  up 
to  23,000  Ibs.  per  square  inch,  and  it  is  an  absurd  waste 
of  material  to  use  a  low  unit  strain  for  the  exceptional 
circumstances  of  extreme  loading.  Power-riveting  is  so 
superior  in  all  respects  to  hand-riveting  that  a  higher 
unit  of  strain,  by  probably  10  per  cent,  can  be  used 
under  the  former  system ;  so  that  if  it  is  considered 
proper  to  strain  hand-riveted  work  up  to  13,500  Ibs.  per 
square  inch,  work  riveted  up  by  steam  or  hydraulic 
power  can  be  safely  proportioned  on  a  basis  of  15,000  Ibs. 
per  square  inch. 

For  convenience  of  selection  of  rivets,  the  following 
table  has  been  prepared,  giving  the  working  values  of 
different  sized  rivets,  in  pounds,  for  plates  of  varying 
thickness,  and  for  different  units  of  strain  per  square  inch. 
Rivet-holes  are  punched  or  drilled  -^  inch  larger  than 
the  rivets,  and  if  the  holes  are  properly  filled,  as  they  can 
be  by  power-riveting,  their  effective  diameter  is  corre- 
spondingly increased. 


THICKNESS  OF  \N 

rEB  PLATES. 

SIZE  OK  RIVETS. 

For  10,000  Ibs.  per  sq. 
inch. 

For 

12,000  Ibs.  per  sq. 
inch. 

tot  15,000  Ibs.  per  sq. 
inch. 

] 

* 

ft 

«J* 

« 

X 

& 

» 

A 

-/, 

*lft 

« 

''<  i  * 

Lbs 

[,bs 

Lbs  Lbs 

Lbs 

Lbs 

Lbs 

Lbs 

Lbs 

Lbs 

Lbs|  Lbs 

Lbs 

Lbs 

!Lbs 

%  inch. 

125011560 

1560  1950  2340 
1875  2340  2810  3280 
2190  2810  3280  3830 
'2500  3125  3750  4375 

375° 
4375 
5000 

1500  1875 
1875  2350 
2250  2810 
2630  3290 
3000  3750 

2810 
3380 
?94o 
4500 

3940 
4600 
5250 

4500 

1875:2350 
2350  2930  3510 
2810  3510  4220 
3280  4100  4920 
[3750,4690,5630 

4920 
5740 
6560 

5630 
£560 
7500 

STRAINS    IN    TRUSSES. 


STRAINS  IN  TRUSSES. 


119 


In  the  following  discussion  of  this  subject  no  attempt 
will  be  made  to  go  beyond  the  ordinary  forms  in  constant 
use,  since  to  do  so  would  be  foreign  to  the  object  of  the 
writer,  as  explained  in  the  preface.     So  many  excellent 
treatises  have  been  written  on  this  subject,  that  any  stu- 
dent desirous  of  going  beyond  these  elementary  pages 
has  a  large  field  to  choose  from.     Probably  the  best  gen- 
eral work  on  the  subject  is   that  of  Mr.  S.  H.  Shreve 
(published  by  D.  Van   Nostrand,  New-York),  inasmuch 
as  the  method  of  analysis  therein  adopted  refers  all  forms 
of  trussing  to  the  principle  of  the  lever,  no  special  analy- 
sis being  employed  for  each  case  as  it  arises.     The  de- 
velopment of  a  subject  from  one  simple  root  or  principle 
permits  of  an  intellectual  grasp  of  that  subject  impossi- 
ble to  attain  by  the  discussion  of  its  separate  topics  in  an 
independent  manner,  even  if  independent  analysis  were 
more  readily  performed.     It  is  not  one  of  the  least  of  the 
beauties  of  the  method  of  the  lever  that,  its  elementary 
principles  being  once  mastered,  it  can  be  immediately  ap- 
plied to    any  system  of  trussing   without   reference   to 
formulae,  and  is  therefore  an  immense  relief  to  the  memory. 
It  is  believed  that  in  the    previous  discussion   of  the 
strength  of  beams,  the  principle  of  the  lever  has  been  so 
thoroughly  kept  in  view  that  its  application  to  truss  forms 
will  be  readily  appreciated.     Before  so  applying  it,  how- 
ever, it  is  necessary  to  explain  some  elementary  ideas  of 
the  composition  and  resolution  of  forces. 


I2O  IRON    HIGHWAY    BRIDGES. 

The  composition  of  a  force  is  the  operation  of  finding 
a  single  force  whose  effect  is  equivalent  to  two  or  more 
single  forces,  while  the  resolution  of  a  force  is  the  con- 
verse operation,  being  the  operation  of  finding  two  or 
more  forces  the  equivalent  of  a  given  single  force.  In 
mechanics,  forces  are  represented  by  straight  lines,  both 
as  to  magnitude  and  direction,  by  taking  the  lines  propor- 
tional to  the  forces  which  they  represent.  What  is  called 
the  parallelogram  of  forces  is  as  follows :  "  If  two  forces 
be  represented  in  direction  and  intensity  by  the  adjacent 
sides  of  a  parallelogram,  their  resultant  will  be  repre- 
sented in  direction  and  intensity  by  that  diagonal  of  the 
parallelogram  which  passes  through  their  point  of  inter- 
section." Thus  in  Fig.  41  the  two  forces  are  represented 
by  the  lines  P  and  Q  applied  to  a  material  point  O. 


FIG.    41. 

Then  the  same  effect  will  be  produced  on  that  point  if 
the  two  forces  are  removed  and  the  diagonal  R,  called 
the  resultant,  substituted.  If  the  diagonal  force  is  exert- 
ed in  the  direction  of  the  arrow,  motion  will  result.  If 
in  the  contrary  direction,  P  and  Q  supposed  to  be  in 
action  as  shown,  there  is  rest  or  equilibrium.  It  will  be 
noticed  that  a  triangle  can  be  substituted  for  the  par- 
allelogram, by  laying  off  from  Q  a  line  equivalent  and 


FORCES    REPRESENTED    BY    LINES.  121 

9 

parallel  to  P,  when  the  resultant  is  at  once  obtained  by 
drawing  a  line  from  the  end  of  P,  thus  transferred,  to  O, 
and  it  is  in  this  form  that  the  parallelogram  of  forces  is 
usually  applied.  Thus  modified,  we  have  what  is  called 
the  triangle  of  forces,  and  the  law  that  "  If  three  forces 
acting  at  one  point  balance,  three  lines  parallel  to  their 
directions  will  form  a  triangle,  the  sides  of  which  are  pro- 
portional to  the  forces,  both  in  direction  and  inten- 
sity." Thus  if  there  are  three  forces,  P,  Q,  R,  Fig. 
42,  acting  at  the  point  O,  and 
if  we  draw  to  any  scale  A  B 
parallel  to  R  ;  A  C  and  B  C 
parallel  to  P  and  Q,  the  sides 
of  the  triangle  thus  formed 
will  be  proportional  to  the 
amounts  of  the  forces  P,  Q,  pIGe  42< 

and  R.  If  R  is  known,  then  B  and  C  may  be  scaled  off 
or  computed  from  the  geometrical  relation  of  the  sides 
of  a  right-angled  triangle.  A  C  and  B  C  are  called  the 
vertical  and  horizontal  components  of  A  B,  or  the  equiv- 
alent effect  of  A  B  in  a  vertical  or  horizontal  direction. 
Any  force  acting  at  an  angle  can  be  determined,  therefore, 
if  we  know  either  component  and  the  angle  of  inclina- 
tion from  the  simple  relation  of  the  parts  of  a  triangle. 
Thus  far  we  have  spoken  of  force,  but  in  reality  we 
know  nothing  of  force  itself,  but  only  the  effects  which  it 
produces.  These  effects  in  structures  are  called  strains, 
which,  when  acting  in  the  direction  of  the  length  of  any 
bar  or  member  of  a  frame,  are  called  longitudinal  strains. 


122 


IRON    HIGHWAY    BRIDGES. 


Let  A  B.  Fig.  43,  be  a  known  vertical  effect  of  a  force, 
A  and  let  the  geometrical  relations  of  the 
lines  of  the  triangle  be  also  known. 
Then  the  longitudinal  strain  in  A  C  will 
exceed  the  vertical  strain  in  A  B  by  the 
number  of  times  A  B  is  contained  in  A  C. 
For  example,  assume  a  right-angled  tri- 
ne. 43.  angle,  the  relations  of  whose  sides  are  6, 
8,  and  10,  and  suppose  the  effect  of  force  on  A  B  has 
been  to  produce  a  strain  of  w  Ibs.,  then  the  longitudinal 
strain  in  AC  is  w  Ibs.  multiplied  by  J^,  or  \\  times  the 
vertical  strain.  The  strain  on  C  B  will  be  similarly  -| 
times  w,  or  f  the  vertical  strain.  For  a  wonderfully 
clear  and  elaborate  discussion  of  force,  strains,  etc.,  as 
well  as  upon  the  subject  of  trusses  and  strength  of  mate- 
rials, freed  from  all  technicalities,  the  learner  is  referred  to 
Mr.  Trautwine's  "  Engineer's  Pocket-Bock,"  a  work  that 
should  be  the  corner-stone  of  every  engineer's  library. 


FIG.  44.    (See  page  35.) 

THE  KING  POST  TRUSS. — The  extreme  effect  on  all 
parts  of  this  form  of  truss  occurs  when  loaded  with  the 
combined  live  and  dead  loads.  In  the  construction 
shown  in  the  figure,  one  half  the  whole  load  rests  upon 
the  cross-beam  upheld  by  the  kingbolt,  the  other  hall 


STRAINS    IN    THE    KING    POST    TRUSS.  123 

• 

being  carried  by  the  abutments  directly,  and    does   not 
affect  the  truss  at  all. 

Call  the  span  //  the  height, /*/  load  per  foot,  w, 
whence  total  load  =  Iw  =  W.  For  equilibrium  the  mo- 
ment of  the  external  forces  must  be  equal  to  the  mo- 
ment of  the  internal  forces.  The  external  force  is  the 
reaction  of  the  abutment,  or  J  wl ;  the  internal  force  is 
the  strain  on  the  material.  Taking  moments  around 
the  foot  of  the  kingbolt,  we  have  for  the  thrust  in 
either  rafter :  Reaction  multiplied  by  its  lever  =  thrust 

multiplied  by  its  lever,  or  ^  X  -  —  T  X  h'  and  T  =  ^- 

For  the  pull  on  the  tie-beam,  moments  must  be  taken 
around  the  apex  of  the  rafters.  Reaction  multiplied  by 

lever  =  pull  multiplied   by  lever,   or  j  X  j  =  P   X  h 

wt* 

and  P  =  -gr 

The  strain  on  the  kingbolt  is  simply  the  load  upheld 
by  it,  or  ^  wl.  If  instead  of  carrying  the  load  on  hori- 
zontal stringers  supported  midway  by  a  cross-beam,  in 
turn  held  up  by  the  kingbolt,  as  in  the  example,  it  is  dis- 
tributed over  the  tie  by  numerous  transverse  beams, 
then  the  tie,  in  addition  to  the  pull  on  it  from  the  thrust 
of  the  rafters,  must  be  proportioned  as  an  ordinary  beam 
exposed  to  a  uniformly  distributed  load  of  \  wl  for  each 
half  of  the  tie.  If  this  truss  is  turned  upside  down,  the 
value  of  the  strains  will  remain  as  it  was  before,  only 
being  reversed  in  kind;  that  is,  the  kingbolt  will  be- 
come a  post,  suffering  compression,  as  does  the  horizon- 


124 


IRON    HIGHWAY    BRIDGES. 


tal  chord,  and  the  diagonals  undergoing  tension  will  be- 
come ties. 

THE  QUEEN  POST  TRUSS  (Fig.  45). — The  load  is  sup- 
posed to  be  carried  from  panel-point  to  panel-point  by 
means  of  stringers,  thus  avoiding  cross-strain  on  the 
horizontal  chord. 

... Z.... 


FIG.  45. 

Call  span  //  depth  truss,  h  ;  w  load  per  ft.  =  wl,  total 
load;  each  panel  \L  Excepting  on  dotted  diagonals, 
maximum  strains  occur  when  load  is  on  both  posts. 
Reaction  of  either  abutment  will  be  half  the  load  sup- 
ported by  the  truss,  or  the  load  on  one  post  —  \wL  For  the 
horizontal  strain  of  compression  in  the  top  chord,  engen- 
dered by  the  pull  of  the  end  diagonals,  take  centre  of 
moments  around  the  foot  of  either  post.  The  forces 
in  action  are  the  reaction  of  either  abutment  and  the 
strain  on  the  material,  the  lever-arm  of  the  former  being 
one  panel-length,  and  of  the  latter  the  depth  of  the 
truss.  As  these  forces  must  balance,  there  results 
^  x  L  =  T  X  h,  or  thrust  =  —'  The  pull  in  the 
parallel  bottom  chord  will  manifestly  be  of  the  same 
amount.  The  strain  in  the  chords  being  derived  solely 
from  the  end  diagonals,  the  strain  in  the  latter  may  be 


COUNTER    DIAGONALS    OF    QUEEN    POST    TRUSS.       125 

f 

determined  from  it  by  remembering  that  the. chord  strain 
is  the  horizontal  effect  or  the  component  of  either  diag- 
onal, of  which  the  vertical  effect  or  component  is  the 
load  on  the  post,  or  the  abutment  reaction  (page  122). 
Knowing  then  the  horizontal  component,  the  longitudi- 
nal strain  in  the  diagonal  is  given  by  multiplying  this 
component  by  the  length  of  the  diagonal,  and  dividing 
by  the  length  of  the  panel ;  or 
Tension  strain  in  diagonal  -  Hor. thrust  X  I^hofd^ag^ 

length  of  panel 

The  compression  on  the  post  is  simply  the  panel  load 
upon  it,  and  equals,  therefore,  ^  wl. 

The  dotted  diagonals  are  counter-braces,  and  are  only 
brought  into  play  when  but  one  post  is  loaded,  in  which 
case  the  reaction  of  the  abutment  nearest  the  load  is 
twice  as  great  as  that  of  the  other.  This  difference  of 
reactions  yields  unbalanced  horizontal  components  for  the 
main  diagonals,  which  must  be  counteracted  by  a  tension- 
bar,  the  horizontal  component  of  which  must  equal  the 
difference  between  the  horizontal  components  of  the 
main  diagonals.  Thus,  suppose  the  load  of  \  Iw  on  the 
right-hand  post  is  removed ;  the  reaction  of  the  right 
abutment  will  be,  according  to  the  law  of  the  lever,  \  of 
this,  or  \  Iw,  and  that  of  the  left  abutment  will  be  f  of 
the  panel  load,  or  f  Iw.  The  horizontal  component,  or 
the  chord  strain  from  the  left  diagonal,  is 

\-lw  X  i  /  divided  by  h  =  ~^>  and  for  the  right  dia- 
gonal this  component  is  \  Iw  x  i  I  divided  by  h  =  ^. 


126  IRON    HIGHWAY    BRIDGES. 

The  difference  between  these  two  values  is  ^T  of  -p 
and  is  the  horizontal  component  of  the  counter  diagonal 
sought.  Its  longitudinal  strain  is  found  as  before  for  the 
main  diagonal  braces,  by  multiplying  the  component  just 

found  by  its  length,  j/J-  /8  +  /?,  and  dividing  the  product 
by  the  panel-length,  or  \l-\  or, 

Maximum  counter-strain  of  tension  =  -^  X  yBS£ 
If  the  load  is  distributed  over  the  whole  upper  chord 
instead  of  being  concentrated  at  panel-points,  to  the 
longitudinal  thrust,  due  to  its  position  in  the  truss,  must 
be  added  the  requirements  of  a  beam  uniformly  loaded. 
As  the  Queen  Post  truss  is  the  parent  of  the  most  usual 
forms  of  truss  met  with,  the  following  numerical  ex- 
ample is  given  of  the  application  of  the  preceding  prin- 
ciples : 

Data.  —  /=  45  ft;  \l  —  panel-length  =  15  ft;  truss 
5  ft.  deep. 

w  =  300  Ibs.  per  ft.  =  4500  Ibs.  per  panel  =  dead  load  j  =  ^^    lbg     iQ^ 
w  =2000-        «     =30,000  «  =    live  load)  panel  load. 

Length  of  diagonal  —  15.81  ft.     Abutment   reaction 
when  wholly  loaded,  34,500  Ibs. 
Strain  on  horizontal  chords  —  T 

tvlz        2300  x  Aj2  ,, 

—  Tr  ^^TS""     :  103,500  Ibs.  compression  upper  and  ten- 
sion lower. 

Strain  on  post— 
\wl=  \  2300  X  45  =  34,500  Ibs.  compression. 

Strain  on  end  diagonals— 


T  x  -  =  103,500  X  -        =  109,089  tension. 


THE    WHIPPLE    TRUSS. 


127 


Strain  in  counter-braces,  one  post  unloaded.  In  this 
case,  as  the  dead  load  is  unchangeable,  we  are  concerned 
with  the  live  load  alone,  or  2000  Ibs.  per  ft.  =  30,000  Ibs. 
per  panel.  The  reaction  of  the  left  abutment  from  this 
(supposing  the  post  to  the  right  is  unloaded)  is  20,000 
Ibs.,  and  of  the  right  abutment  10,000  Ibs. 

Horizontal   strain  from    left  diag-^ 

onal,  —  -  =  60,000 

TT     •  •     r          •  i^  j-        Vdiff.  30,000. 

Horizontal  strain  from  right  diag- 

,      10,000  X    1C 

onal, =  30,000 

This  difference  being  horizontal  difference,  for  conver- 
sion into  longitudinal  strain  on  the  counters,  it  is  to  be 
multiplied  as  before  by  -~r>  which  gives  31,620  Ibs.  as 
tension  on  the  counters;  or  by  applying  the  formula, 
the  strain  is  at  once  given— 

/2  w  A  724-7,2  452  x  2000     _    1581          mnr\r\    V     T^C/I 

=  30,000  x  1.054  — 


THE  WHIPPLE  TRUSS  (Fig.  46). — By  extending  the 
Queen   Post  so    as  to    embrace  additional   panels,  the 


128  IRON    HIGHWAY    BRIDGES. 

Whipple  truss  is  developed,  as  in  the  figure  representing 
the  diagram  of  a  through-bridge  having  seven  panels. 

Let  /  =  span ;  n  —  number  panels ;  /i  =  height  of 
truss ;  w  dead  load  at  each  panel-point ;  w'  =  varia- 
ble load  on  one  panel. 

ist.  Chord  Strains. — Maximum  strain  in  chords 
occurs  when  all  panels  are  loaded  with  dead  and  live 
loads,  in  which  case  reaction  of  either  abutment  is 

---—  — '  or  three  panel  loads  =  3  (w  +  w'\  For  first 
panel,  horizontal  strain  will  be  (moments  around  d  as  a 
fulcrum)  3  (w  +  «/)  X  —  -*-  /z,  or  reaction  multiplied  by 
lever  of  one  panel-length,  divided  by  depth  of  truss. 
For  third  panel  be,  the  strain  will  be  (moments  around  b) 
(3  (w  +  a/)  X  ^  -  -  (w  +  w')  X  ^)  -*-  A.  In  this  ex- 
pression it  will  be  noticed  that  one  panel  load  multiplied 
by  its  lever  of  one  panel  is  subtracted  from  the  moment 
of  the  reaction.  This  is  because  the  weight  at  a  operates 
downward  or  contrary  to  the  reaction  of  the  abutment, 
as  shown  by  dotted  lines,  and  reduces  correspondingly 
the  effect  of  abutment  reaction.  On  the  middle  panel 
eg,  the  horizontal  strain  will  be  (3  (w  +  w')  X  ^  ~~  (w 

+  w  ~)  --  (w  +  wf)  -)  +  AS  or,  in  other  words,  subtract 
from  the  moment  of  the  reaction — operating  in  one  direc- 
tion— the  moments  of  the  panel  loads  between  fulcrum 
and  abutment,  and  then  divide  by  the  depth  for  the 
strain. .  The  same  process  must  be  continued  for  any 
number  of  panels  up  to  the  centre  of  the  truss  where 
the  strains  are  a  maximum,  after  which  they  decrease  to 
the  other  abutment.  While  the  chord  strains  are  the 


STRAINS    IN    WHIPPLE    TRUSS.  129 

same  top  and  bottom,  they  are  not  so  for  the  same  panel. 
The  inclination  of  the  diagonals  brings  the  panels  of 
equal  strain  in  advance  of  each  other ;  that  is  to  say, 
the  tension  strain  in  b  c  is  the  same  as  the  compressive 
strain  in  d  e,  c  g  as  in  e  f.  The  example  given  is  for  an 
uneven  number  of  panels,  in  which  case  there  will 
be  three  panels  of  the  top  chord — namely,  the  centre  and 
one  either  side,  of  equal  maximum  strain,  to  one  panel  of 
maximum  strain  at  the  centre  of  bottom  chord.  If  a 
diagram  is  made  for  an  even  number  of  panels,  there 
will  be  a  post  at  the  centre,  and  it  will  be  seen  that  the 
maximum  strain  on  top  chord  will  extend  over  two 
panels,  one  on  either  side  of  centre,  and  will  be  in  excess 
of  the  maximum  strain  in  the  bottom  chord,  owing  to 
the  main  diagonals  of  the  two  middle  panels  uniting  at 
the  foot  of  the  post  where  their  horizontal  components 
balance  each  other.  At  the  top  chord,  however,  these 
diagonals  are  spread  apart  two  panel-lengths,  and  deliver 
their  horizontal  component  to  that  chord. 

Example. — Let  /  —  70  ft. ;  n  =  7  ;  h  =  io  ft. ;  w  = 
300  Ibs.  ft.  =  3000  Ibs.  per  panel;  w'  =  1000  Ibs.  ft.  = 
10,000  Ibs.  per  panel ;  w  +  w'  =  13,000;  abutment  re- 
action =  one  half  of  six  panel  loads  =  39,000  Ibs. 

The  horizontal  strain  on  O  a  and  a  b  will  be 
3^0™  =  39>000  lbs> 

The  horizontal  strain  on  d  e  and  b  c  will  be 

39,000  x  20  —  13,000  x  io  /:  -  OOO  Ibs 

io 

The  horizontal  strain  on  e  f,f  h,  h  z\  and  eg  will  be 

39,000  x  30  -  13,000  x  20  —  13,000  x  io    __    ygoQO 
io  "  /•  « 


I3O  IRON    HIGHWAY    BRIDGES. 

2d.  Web  Strains. — The  web  strains  must  be  com- 
puted  separately  under  each  condition  of  loading.  The 
posts  and  braces  are  strained  the  greatest  when  the 
moving  load  covers  the  segment  from  which  any  given 
diagonal  slopes.  Thus  the  diagonal  e  c  is  strained  the 
greatest  when  c  and  all  points  to  the  right  are  loaded 
with  moving  load  ;  f  g  when  g  and  all  points  to  its  right 
are  loaded,  etc.  While  the  web  strains  can  be  readily 
calculated  by  finding  the  horizontal  components  for 
each  maximum  condition  of  loading,  and  converting 
them  into  longitudinal  strains,  as  was  done  for  the 
Queen  Post  truss,  the  method  is  somewhat  tedious  when 
there  are  a  number  of  panels,  and  a  separation  of  dead 
and  live  loads  must  be  made.  For  trusses  with  parallel 
chords,  the  following  method  will  be  found  most  conve- 
nient, and  is  the  one  usually  employed.  It  is  based  on 
considering  the  load  on  each  panel-point,  tracing  its  action 
on  the  posts  and  ties,  and  summing  their  effects — or,  in 
other  words,  finding  the  vertical  components,  which  are 
the  post  strains.  Taking  first  the  dead  load,  there  is  w 
at  each  panel-point,  or,  under  the  example,  3000  Ibs. 
Since  three  panel  loads  are  supported  by  each  abutment, 
the  loads,  and  therefore  the  strains,  are  symmetrical  with 
the  centre,  and  it  is  only  necessary  to  compute  the 
strains  for  one  half  the  truss.  At  the  point  c,  3000  Ibs. 
is  taken  up  by  the  inclined  tie  e  c,  and  delivered  to  the 
vertical  post  e  b,  which  has  a  compression,  therefore,  of 
that  amount ;  the  tension  on  the  tie  being  3000  Ibs.  X 

its  length  14.1  ft.  1t  r^\  •  i  i       j 

depth  of  truss*  or  3O°o  X  7^7  =  4230  Ibs.     This  panel  load 


STRAINS    IN    WHIPPLE    TRUSS.  131 

• 

is  again  progressed  to  the  abutment  by  the  tie  d  b,  which 
also  has  upon  it  another  panel  load  at  b  of  3000,  making 
6000  Ibs.  delivered  to  the  end-post  d  o.  The  strain  on 
this  tie  is,  therefore,  just  double  that  on  the  preceding 
tie,  or  8460  Ibs.,  to  which  must  be  added  the  effect  of 
the  third  panel  load  sustained  by  the  vertical  tie  d  a,  or 
4230  Ibs.  for  the  compressive  strain  for  the  inclined  end- 
post,  making  a  total  for  that  post  of  12,690  Ibs.  For 
the  moving  load  alone,  advancing  from  the  left  abut- 
ment, we  have,  when  it  reaches  the  points,  10,000  Ibs. 
By  the  law  of  the  lever,  %  of  this  is  supported  by  the  left 
abutment,  and  \  by  the  right  abutment.  Since  the  whole 
of  this  load  ascends  the  vertical  a  d,  the  \  that  goes  to 
the  right  can  only  do  so  by  passing  down  the  diagonal 
d  b  to  the  foot  of  the  post  e  b,  when  the  diagonals  in  the 
opposite  direction  progress  it  toward  the  right  abutment. 
The  strain  in  d  b  from  this  action  of  the  load  is  one  of 
compression ;  but  since  the  dead  load  strains  this  diag- 
onal tensively  largely  in  excess  of  this  compressive  effect, 
the  latter  is  entirely  neutralized.  Advancing  to  each 
panel-point  in  succession  with  the  load  of  10,000  Ibs., 
and  distributing  the  load  by  the  law  of  the  lever,  the 
strains  on  the  various  parts  will  be  as  follows,  from  the 
live  load  alone : 

On— od:\  (6  +  5+4  +  3  +  2  +  1)  io,oooXJTV  compression  =  42,300 
ad:      one  panel  load,  tension  =10,000 

db:  M5+4  +  3  +  2  +  1)  i°,°°oXJ^-J  =30,214 

e  b:  |  (4  +  3  +  2  +  1)   10.000  compression^  14,280 

ec:      sameas*£x-W  tension          =20,143 


132 


IRON    HIGHWAY    BRIDGES. 


fc: 

fg-' 
hg: 
hj: 


10,000 
sameas/<rx:l^1 
same  maximum  as  fc 


compression^  8,571 
tension  =12,086 
compression^  8,571 
tension  =  6,040 


If  to  these  are  added  the  previously  computed  effects 
of  the  dead  load,  there  result  the  maximum  strains  that 
can  come  upon  the  web  system  by  any  possible  condition 
of  loading. 

Since  the  counter  diagonals  can  only  act  when  the 
main  diagonals  of  the  same  panel  are  relaxed,  it  follows 
that  to  obtain  the  maximum  tension  of  any  counter,  the 
effect  of  the  dead  load  to  which  it  is  opposed  must  be 
subtracted  from  the  effect  due  to  the  live  load  alone. 
Thus,  counter  hj  is  strained  from  the  live  load  6040  Ibs., 
but  main  diagonal  g  i  is  strained  by  the  dead  load  4230 
Ibs  ;  therefore  the  counter  is  to  be  proportioned  for  6040 
less  4230  Ibs.,  or  only  1810  Ibs. 

In  the  case  of  the  Whipple  double-cancelled  truss, 
each  system  of  the  web  must  be  computed  independent 
of  the  other,  and  their  ioint  effect  on  the  chords  added. 


I 


c 


i 


Cf 


FIG.  47. 


WARREN  GIRDER  (Fig.  47). — Load  supposed  to  be 
concentrated  at  the  panel-points  of  the  top  chord. 


THE    WARREN    GIRDER. 


133 


Span,  60  feet;  6  panels  of  10  feet.  Truss,  10  feet 
depth.  Length  diagonal,  i  i.i  8  feet.  Dead  load  per  panel, 
3000  Ibs.  Moving  load  per  panel,  9000  Ibs.  Reaction 
of  abutment  for  full  loading  (.so_o  o.:j3JLo  o.)  x  5  panels 
=  30,000  Ibs. 

FOR  CHORD  STRAINS,  the  centre  of  moments  must  be 
taken  alternately  on  top  and  bottom  at  panel-points.  It 
will  be  noticed  that  at  each  panel-point,  owing  to  the 
inclination  of  the  web  members,  there  is  a  horizontal 
effect  from  each  member,  acting  in  the  same  direction. 

^  .  30,000  Ibs.   x  5  ft. 

Compression  on  a,  -      ~~fo~fT~      -  =    .     .     .     15,000  Ibs. 

rr*  •  T  3O,OOO  Ibs.    X    IO  ft. 

Tension  on  0,  ~ro~ft~        =      .    .    .     30,000   ' 

^  •  »  30,000  Ibs.  x  15  ft.—  12,000  x  5 

Compression  on  c,  -  I0  -  —    39,000 

rr^  ,  .  3O,OOO    X     2Q    —    I2.OOOXIO 

Tension  on  at  ~7o~~  •     4°,ooo   ' 

^  .  SO.OOOv 2 5  -•  I2.OOOX5  —  I2.OOOXI5 

Compression  on  e,  ~IO-  -  =  51,000   ' 

rr^  •  /•  30,000X30-12,000X10-12,000X20  _,   .  rvv<l      « 

Tension  on/,  ~~^~~  -54,000 

The  preceding  operation  is  simply  putting  in  figures 
the  oft-repeated  principle  of  the  lever.  In  each  case  the 
numerators  of  the  fractions  may  be  read, "  The  reaction  of 
abutment  (upward)  multiplied  by  its  lever,  less  the  sepa- 
rate panel  loads  (downward)  between  abutments  and 
fulcrum,  multiplied  by  their  levers  ;"  while  the  denomi- 
nator is  the  depth  of  truss,  which  is  the  leverage  of  re- 
sistance. 


134  IRON    HIGHWAY    BRIDGES. 

FOR  WEB  STRAINS. — ist.  Dead-load.  One  half  of 
that  at  central  apex,  or  1500  Ibs.,  goes  down  diagonal  6, 
up  5,  down  4,  which  receives  in  addition  a  full  panel-load, 
making  3000  +  1500  Ibs.,  which  goes  up  diagonal  3,  being 
again  increased  before  passing  down  2,  \vith  another 
panel-load,  or  3000  +  3000  +  1 500  Ibs.,  which,  in  turn, 
passes  up  diagonal  i  to  point  of  support.  The  diagonals 
to  right  of  centre  are  traversed  by  the  load  on  that  side 
in  the  same  way.  These  vertical  effects  need  only  to  be 

,   .    ,.     .  ,        length  of  diagonal  ,  ,       c       , 

multiplied  by  -  heigh"  "  to  &lve  tne  sought-for  longi- 
tudinal strains  in  the  diagonals  due  to  dead-load.  When 
the  load  passes  down,  compression  is  induced  ;  and  when 
up,  tension.  Thus,  i,  3,  and  5  are  in  tension,  and  6,  4, 
and  2  are  in  compression.  2d.  Variable  load.  Com- 
mence by  loading  the  first  apex  on  the  left  with  moving 
panel-load  9000  Ibs. ;  of  this  -J  is  supported  by  the  left 
abutment,  and  ^  by  the  right  abutment.  These  propor- 
tions of  the  load  only  reach  their  destination  by  passing 
down  and  up  alternately  the  different  web  members,  in- 
ducing compression  and  tension  alternately.  Tracing 
out  the  effect  of  each  load  (/,  q,  r,  st  /)  in  succession, 
commencing  at  the  left  apex,  the  vertical  effect  on  diago- 
nals will  be  as  follows : 


$/  +  6  7  +  6^+  i*/"^'ir'*W  produce  tension  on  i. 
f /  +^1?  +  I*  +  t~*  +  i*  H        "         compression  on  2. 
3  receives  a  compression  from  £  the  load  at  /,  and  tension  from  all  loads  to 
the  right,  amounting  to  $  q  +  %  r  +  |  s  +  %  *• 


STRAINS    IN    THE    WARREN    GIRDER.  135 


• 


Diagonal  4  has  tension  from  £  /,  and  a  compression  from  f?  4-  |  r  +  f  /  +  $  /. 

5  "  compression  from  &/  +  £?,  and  a  tension  from  -g  r  +  §•  s  +  £  /. 

"        6  "  tension  from  £/  +  I  g,  and  a  compression  from  %r+$s  +  %t 

"        7  "  compression  from  £/  +  §  <7  +  §  r,  and  a  tension  from  £  s  + 

"        8  "  tension  from  £/  +  $?  +  §  r,  and  a  compression  from  $s  + 

9  "  compression  from  \p  +  %q  +  |  r  +  £  j,  and  a  tension  from 

"      10  "  tension  from  %p  +  %q  +  f  r+  $  s,  and  a  compression  from 

"      ii  "  compression  from  £/  +  f  f  +  f  r  +  f  *  +  }  /,  no  tension. 

"      12  "  same  as  n,  only  tension. 


Summing  these  effects  of  the  moving  load,  and  re- 
membering that  the  loads  at  each  apex  are  the  same  in 
amount,  or  9000  Ibs.,  -J-  of  which  is  1500  Ibs.,  which,  con- 
verted into  longitudinal  effect,  is  1500  X  "j^ft"  —  1677 
Ibs.,  we  have  for  the  strains  in  the  web  : 


Diagonal  i.  15  y  1677  =  25,155  Ibs.  tension. 

"  2.  15  x  1677  =  25>!55  Ibs.  compression. 

"  3.  10  x  1677  =  16,770  Ibs.  tension,  and  I  x  1677  —  1677  Ibs.  comp. 

"  4.  10  x  J677  =  16,770  Ibs.  comp.,  and  I  x  1677  =  1677  Ibs.  tension. 

"  5-  6  x  1677  =  10,062  Ibs.  tension,  and  3  x  1677  =  5031  Ibs.  comp. 

"  6.  6  x  J677  =  10,062  Ibs.  comp.,  and  3  x  J677  =  5931  Ibs.  tension. 

"  7.  6  x  1677  =  10,062  Ibs.  comp.,  and  3  x  1677  =  5931  Ibs.  tension. 

"  8.  6  x  J677  =  10,062  Ibs.  tension,  and  3  x  J677  =  5931  Ibs.  comp. 

"  9.  10  x  1677  =  16,770  Ibs.  comp.,  and  I  x  1677  =  1677  Ibs.  tension. 

"  10.  10  x  J677  =  16,770  Ibs.  tension,  and  I  x  J677  =  1677  Ibs.  comp. 

"  ii.  15  x  1677  =  25,155  Ibs.  comp. 

"  12.  15  x  1677  =  25,155  Ibs.  tension. 

To  the  above  values  must  be  added,  for  final  maximum 
web-strains,  the  effect  of  the  permanent  load,  3000  Ibs., 
at  each  apex,  which,  converted  into  longitudinal  effect  as 
above,  is  3354  Ibs.  This  is  done  in  the  following  table : 


I36 


IRON    HIGHWAY    BRIDGES. 


NAME 

OF 

FROM  MOVING  LOAD 

ALONE. 

FROM  DEAD  LOAD 

ALONE. 

ALGEBRAIC 
SUM  OF  MOVING  AND 
DEAD  LOAD. 

DIAGO- 

NAL. 

_J_ 

i 

_|_ 

Com- 
pression. 

Tension           Com" 
pression. 

Tension. 

Com- 
pression. 

Tension. 

Ibs. 

Ibs.        j       Ibs.              Ibs. 

Ibs.        |        Ibs. 

i 

.... 

25,155 

.... 

8,385 

j 

33,540 

2 

25,155 

.... 

8,385 

.... 

33,540 

none 

3 

1,677 

16,770 

.... 

5,031 

none 

21,801 

4 

16,770 

i,677 

5,031 

.... 

21,801 

none 

5 

5,031 

10,062 



1,677 

3,354 

n,739 

6 

10,062 

5,031 

1,677 

n,739 

3,354 

7 

10,062 

5,031 

1,677 

.... 

n,739 

3,354 

8 

5,031 

10,062 

.... 

i,677 

3-354 

u,739 

9 

16,770 

1.677 

5,031 

21,801 

none 

•   10 

1,677 

16,770 

.... 

5-031 

none 

21,801 

ii 

25,155 

.... 

8,385 

33,540 

none 

12 



25,155 

.... 

8,385 



33-540 

It  will  be  seen  from  the  above  table  how  the  com- 
pression due  to  the  variable  load  in  diagonals  10  and  3 
is  more  than  neutralized  by  the  tension  from  the  fixed 
load.  Diagonals  5,6,  7,  and  8,  however,  must  be  capable 
of  acting  either  by  tension  or  compression,  since  the 
effect  of  the  variable  load  preponderates  over  the  dead 
load  that  works  against  it.  In  other  words,  the  necessary 
counterbracing  is  confined  to  the  last  diagonals  named. 
When  the  span  becomes  so  great  as  to  make  the  tri- 
angles of  the  Warren  system  too  large,  another  series 
may  be  introduced,  each  one  being  computed  indepen- 
dently of  the  other,  care  being  taken  not  to  omit  their  joint 
effect  on  the  chords.  By  increasing  the  number  of  sys- 
tems of  triangles,  the  lattice-truss  is  formed ;  but  this  is 


FINK    SUSPENSION    TRUSS. 


137 


not  a  commendable  form  of  truss,  since  the  intersections 
of  the  different  systems  must  be  riveted  together,  which 
vitiates  more  or  less  the  calculations,  based,  as  they  neces- 
sarily must  be,  upon  the  hypothesis  of  an  independent 
action  of  each  system  of  triangles. 


FIG.  48. 

THE  FINK  SUSPENSION  TRUSS  (Fig.  48). — This  form 
of  truss  is  only  well  adapted  for  deck  spans,  and  is  pre- 
cisely the  same  truss  as  the   ordinary  iron  roof  turned 
upside  down,  with  the  reversal  of  the  quality  of  strains. 
The    maximum    chord    strains    and    all    parts   of    the 
primary  system  (marked  i)  occur  when  all  points  are 
loaded.    On  the  secondary  system  (marked  2),  maximum 
strains  occur  when  all  the  panels  embraced  in  that  system 
alone  are  loaded,  and  so  on.     Let  the  load  on  each  apex 
be  w,  then  posts  3  support  w  only ;  posts  2  support  w  + 
-J-  w,  delivered  to  it  from  each  sub-post  3,  or  2  w ;  post  i 
sustains  its  own  w,  +  \  of  the  load  on  each  sub-post  2,  + 
\  the  load  from  each  adjoining  sub-post  3,  in  all  4  w. 
The  suspension  rods  are  strained  in  proportion  to  their 

inclination  or  j^^™*-  Example.— Span,  120  feet;  8. 
panels,  1 5  feet ;  height  of  centre-post,  1 5  feet ;  load  on 
each  apex,  10,000  Ibs. ;  ratio  of  length  of  any  rod  to  post 


138 


IRON    HIGHWAY    BRIDGES. 


61.8  ft. 


of  system  to  which  it  belongs,  -|yft>-  —  4.12;  ratio  of 
horizontal  to  vertical,  ff-  —  4. 

i  st.  Strain  on  posts — compression. 

Sub-system,  3  — w=  10,000  Ibs. ;  secondary,  2  —  2  w  = 
20,000  Ibs. ;  primary,  i  -  -  4  w  =  40,000  Ibs. 

2d.  Longitudinal  tension  in  suspension  bars. 

Suspension  bars,  sub-system  i    .     .     .     •£-  10,000  x  4-J2  =  20,600  Ibs. 
"  "     secondary  system  2  .     £  20,000  x  4- 12  =  41,200   " 

"  "     primary  "         3  .     \  40,000  x  4- 12  =  82,400  " 

Strain  in  panel  a  will  be,  therefore,  82,400  Ibs.;  in  b  = 
82,400  +  41,200  =  123,600;  in  c  =  123,600  +  20,600  — 
144,200  Ibs.  The  horizontal  chord  strain  will  be  uniform 
throughout,  and  is  the  sum  of  the  horizontal  compo- 
nents of  the  several  systems. 

From  sub-system  3 \  10,000  x  4  =     20,000  Ibs. 

"      secondary  system  2  ....     \  20,000  x  4  =     40,000     " 
"      primary         "        I ....    ^  40,000  x  4  =     80,000    " 


Total  chord  strain, 140,000  Ibs. 


FIG.  49. 


THE  BOWSTRING  TRUSS  (Fig.  49). — The  maximum 
horizontal  strain  occurs  when  all  panels  are  loaded 
both  with  fixed  and  moving  loads,  and  is  uniform 


THE    BOWSTRING    TRUSS. 


'39 


throughout  the  length  of  the  tie  or  bottom  chord. 
The  longitudinal  thrust  through  the  arch  varies  with 
the  inclination  of  the  arch-segments,  being  equal  in 
amount  to  that  of  the  horizontal  strain  at  the  centre 
only.  To  find  the  horizontal  strain  at  the  centre  under 
uniform  load,  "  multiply  the  abutment  reaction  (in  this 
case  2\  panel-loads)  by  its  lever  or  \  span,  from  which 
subtract  the  intermediate  panel-loads,  multiplied  by  their 
leverages,  acting  in  the  opposite  direction  to  the  reac- 
tion, and  divide  the  result  by  depth  of  truss."  The  ex- 
treme longitudinal  thrust  in  the  arch  occurs  in  the  last 
segment,  being  the  one  of  greatest  inclination,  and  is  at 
once  found  by  "  multiplying  the  reaction  by  the  lever  of 
one  panel-length,  and  dividing  by  the  perpendicular  let 
fall  from  the  point  around  which  the  moments  are  taken 
upon  the  direction  of  the  segment"  Or  the  longitudinal 
strain  in  any  segment  may  be  found  by  multiplying  the 
maximum  horizontal  strain  by  the  length  of  segment, 
and  dividing  by  its  horizontal  stretch. 

In  the  web,  under  uniform  loading,  there  is  no 
other  strain  than  tension  on  the  verticals,  amounting  to 
a  panel-load,  and  the  diagonals  are  unnecessary ;  but 
under  a  variable  load,  moving  from  end  to  end  of  the 
truss,  the  verticals  are  brought  under  a  compressive  strain 
through  the  medium  of  the  diagonals,  the  strain  on 
which  may  be  most  conveniently  computed  as  follows : 
For  each  position  of  the  load  as  it  advances  from  point 
to  point,  determine  the  abutment  reaction  as  for  an  ordi- 
nary truss  on  the  principle  of  the  lever.  From  this 


I4O  IRON    HIGHWAY    BRIDGES. 

compute  the  horizontal  strain  at  the  extreme  point  of 
loading,  and  also  at  the  next  panel-point  beyond.  The 
difference  between  these  two  strains  will  be  the  hori- 
zontal component  of  the  diagonal  of  the  panel  between 
the  points  where  the  horizontal  was  computed.  This 
has  now  to  be  converted  into  the  direction  of  the  diago- 
nal for  its  longitudinal  strain,  from  which  the  vertical 
effect  of  compression  on  the  post  is  readily  derived. 
Since  tension  forever  exists  on  the  verticals  from  the 
dead  load,  the  amount  of  tension  of  one  panel  dead 
load  must  be  deducted  from  the  compression  above 
found  for  maximum  compressive  effect  that  can  come 
on  a  post.  As  an  example  of  the  application  of  these 
principles,  assume  a  bowstring  truss,  with  6  panels  of  1 5 
feet,  and  13  feet  deep  at  centre.  Also  let  dead  load 
w  =  5000  Ibs.  per  panel,  and  live  load  w'  =  15,000  Ibs. 
per  panel.  The  lengths  of  the  verticals  and  diagonals  as 
marked  on  the  diagram  : 

Maximum  horizontal  chord  strain 

Reaction. 


(u>+w')x  2\  panels  x  45  ft. /.  —  (w  + a/)  X  (1  +  2)15  ft..     JQ     g    g  j^g 

Maximum  thrust  in   last   segment  f  g  of  arch  = 

2±  panels  X  15  ft.  20,000  X  2J  +  15  _  ,, 

"~6^"ft.~~  6.7  ^>940     0& 

Maximum  tension  on  verticals  w  +  w  =  20,000  Ibs. 
Constant  tension  from  dead  load  alone  w  —  5,000  Ibs. 
Maximum  tension  on  b  c'  occurs  when  variable  load 
is  at  b  alone ;  reaction  left  abutment  =  -f  w'  =  12,500. 

Horizontal  tension  at  6=***™^=&&°=2 5,000 Ibs. 


THE    BOWSTRING    TRUSS.  14! 

Horizontal  tension  at  c  —I2-5QQ  *  30  —  15.000  x  1 5  _  150,000 

cc  11.7 

=  12,820  Ibs. 

25,000  less  12,820  Ibs.  =  12,180  Ibs.  the  horizontal 
component. 

12,180  X  ff-  ~  longitudinal  tension  in  b  c'  =  15,328. 
Maximum  tension  on  cd',  moving  load  at  b  and  c. 
Reaction  left  abutment  =  £  w'  +  f  w'  =  22,500  Ibs. 
Horizontal  strain  at  c  . .  gjogjj  so-  15.000  x  15  =  3g46o 

Horizontal  strain  atrf  . .  22>5°°  x  45  ~  IS'°°°  x  I5  (I  +  2) 

13 

25,9°°- 

38,460  less  25,900  =  12,560  Ibs.  =  horizontal  compo- 
nent of  c  d. 

12,560  X  f£  =  longitudinal  tension  in  ^^16,713  Ibs. 

Maximum  tension  on  d  e ,  moving  load  at  b,  c,  and  d. 

Reaction  left  abutment  ^-t|i-3  w'  —  30,000. 

Horizontal  strain  at  d  =  3°t000  x  45  ~  I*>™JL1L 

13 


Horizontal  strain  at  e  =  30.000x60-15.^5(1 


51,923  less  38,461  =  13,462  Ibs.,  horizontal  component 
13,462  X  {-§-  =  longitudinal  tension,  17,052  Ibs. 
Maximum  tension  on  e  f  ;  all  points  but  /  loaded 
with  w\ 


Reaction  left  abutment  5  +  4  +  3  +  2  w'  =  35,000. 


TT  i_     1  ' 

Horizontal  strain  at  e  = 
=  64,103. 


35.OOO    X    6O  -  I5,OOO    X     15  (l  -4-  2  +  3) 


142  IRON    HIGHWAY    BRIDGES. 

Horizontal  strain  at/-  3^gggJLJlzii^pj.s(L+  a  +  3  +  4) 

=  50,000. 

64,103  less  50,000  =  14,103  =  horizontal  component 
14,103  x  |f  =  longitudinal  tension  in  ef',  15,983. 

The  compressive  strain  in  verticals  from  a  moving 
load  occurs  when  all  panel-points  between  any  given 
one  and  the  abutment  are  loaded.  Thus  d  d'  is  com- 
pressed the  greatest  when  b  and  c  or  e  and  f  are  loaded. 
The  strain  (supposing  the  load  is  at  b  and  c)  on  d  d1  will 
be  the  vertical  component  from  d  e,  less  the  tension  of 
one  panel  of  dead  load.  It  is  necessary,  then,  to  find  the 
longitudinal  strain  on  the  different  diagonals  when  the 
panel-points  beyond  are  loaded,  and  that  of  the  given 
diagonal  unloaded. 

On  c  d'  ,  when  b  alone  is  loaded,  reaction  =  -|  w'  — 
12,500. 

Horizontal  strain  at  c  =  "•SODJCJS.OOOXJIS  =  1 


d  = 


45  -15.000x30 


12,820  less  8654  =  4166  =  horizontal  component, 
which  multiplied  by  |^  =  5521  =  longitudinal  strain. 
Converting  this  last  strain  into  vertical  strain  by  multi- 
plying it  by  the  ratio  of  diagonal  to  vertical,  or  ^|,  the 
compression  on  post  c  cf  from  line  load  is  obtained. 
Since  there  is  always  a  tension  caused  by  one  panel  of 
dead  load,  the  compression  above  found  must  be  reduced 
by  that  amount,  to  obtain  the  maximum  compression. 


THE    BOWSTRING    TRUSS.  143 

On  d  d'  ,  when  b  and  c  are  loaded,  reaction  =  1  w  = 

o 

22,500. 

Horizontal  strain  at  d=  22'5°°  x  45  ~  I5'°°°  x  'il'-Ji*)  = 

13 


2  5 

Horizontal  strain  at  e  =  2-^^*-6^-^°AI5  (*  +  3)  = 

I9.H5- 

25,963  less  19,145  =  6818  =  horizontal  component. 
Multiplying  this  component  by  -ff-  =  5900;  less  5000  = 
maximum  compression  on  post  d  d'  =  900. 

On  e  e'  ,  when  b,  c,  and  d  are  loaded,  reaction  =  J¥2-  w 
—  30,000  Ibs. 

Horizontal  strain  at 

_  30.000  x  60  -  15,000  x  15  (i  +  2  -f  3)  _   ,,0     s 

11.7  ~  o54DI- 

Horizontal  strain  at 

r  _  30,000  x  75  —  15,000  x  15  (2  H-3  +  4)  _ 
/  -  ~~7.5~  "  3°'Ooa 

38,461  less  30,000  =  8461  horizontal  component. 
Converting  this  horizontal  strain  into  vertical,  there  re- 
sults for  compression  on  posts  from  live  load  8461  Ibs. 
X  ^f  =4230  Ibs.  Since  the  tension  induced  by  dead 
load  is  5000  Ibs.,  there  can,  therefore,  be  no  compression 
whatever  on  post  e  e'. 

On  b  b'  or  f  f,  there  can  be  no  other  strain  than  that 
of  tension  from  w  +  w'. 

If  the  bowstring  is  inverted,  the  strains  may  be  com- 
puted in  the  same  way  as  above  explained,  but  are  re- 
versed in  quality.  The  horizontal  tie  will  become  a 
compression  chord,  and  the  arch  will  be  under  tension. 


144  IRON    HIGHWAY    BRIDGES. 

The  posts,  in  this  case,  will  be  compressed  from  the 
dead  load,  the  effect  of  which  is  therefore  added  to  that 
of  the  diagonals  (being  of  the  same  quality),  instead 
of  being  subtracted  as  before. 

For  a  deck  span  this  adaptation  of  the  bowstring  truss 
is  to  be  commended  as  economical  in  material  and 
pleasing  in  appearance. 


RETUKN  TO 


BORROWED 


LD21 — 32m — 1,'75 
(S3845D4970 


